Detection tests - measurements

.Ks;h
wkdjrK mÍlaIK
DIAGNOSTIC TESTS
ñkqï
.Ks; fomd¾;fïka;=j
úoHd yd ;dlaIK mSGh
cd;sl wOHdmk wdh;kh
Y%S ,xldj

II
b.ekaùu iy bf.k .ekSu
;u mdif,a whym;a ld¾hidOkhla fmkakqï lrk isiqkaf.a bf.kqï ÿIalr;d wkdjrKh
lr .ekSu i|yd .=rejrhdg wjYH jk uQ,sl lreKq fuu fmd; u`.ska iemfha' úIhud,dj
l%shd;aul lsÍfï § .=rejreka isys ;nd .; hq;= lreKla jkafka" Tjqkaf.a l%shdldrlï u`.ska
orejkaf.a nqoaêuh idOkh iy p¾hd j¾Okh fj; iqúYd, jQ;a §¾>ld,Sk jQ;a n,mEula flfrk
nj h'
wOHdmkfha §" úNd.j,g uqyqK §fuka miq ;uka idOkh lr .;a M,fhys i;=g N=la;s
ú£ug isiqkag yels jk fia uQ,sl úIh lreKqj, wfmalaIs; m%ùK;d uÜgï ,nd .ekSu i|yd" ish¨
mdi,a orejkag wjia:djla i,id §u rcfha wfmalaIdj hs'
orejdf.a p¾hd j¾Okh ms<sn| j ie,lSfï § wOHdmkfha wruqK jkafka" nqoaêuh idOkh"
jev f,dalh iu`. iïnkaO lsÍu h' tneúka mdif,ka mßndysr f,dalh iu`. lghq;= lsÍug
YsIHhdg wjYH jk ksmqK;d ixj¾Okh lsÍu msKsi Tjqkag úIhud,dj bÈßm;a lsÍu .=rejrhdf.a
ld¾hNdrh fõ' fï lafIa;%j,g jeo.;a fmdÿ ksmqK;d lsysmhla wh;a fõ'
• ld¾hCIu ld¾h iodpdrh - Okd;aul wdl,am" kfjda;amdok flfrys we;s leue;a;
yd wêIaGdkYS,S j lghq;= lrf.k hdu'
• wka;¾-mqoa., iïnkaO;d - lKavdhï jev" úkh iy M,odhS ikaksfõokh
• m%cd idrO¾u - úúO;ajhg .re lsÍu jeks m%cd .=K O¾uj,ska iukaú;
idOq .=K iïmkak mqoa.,fhla
wjidk jYfhka fuu bf.kqï-b.ekaùï l%ufõoh foi l<ukdlrKfhys i|yka jk 4A
flfrys" tkï wdl,amh (Attirude), úYaf,aIKh (Analysis)" l%shdud¾.(Action)" yd j.ùu
(Accountability)" flfrys wjOdkh fhduq lrk f,i mdi,aj, isák ish¨ u úÿy,am;sjrekaf.ka"
.=rejrekaf.ka yd fjk;a ld¾huKav,j,ska b,a,d isàug uu leue;af;ñ' wjidk m%;sM,h ms<sn|
j WÑ; yd Okd;aul wdl,am iys; j Tn lrk ld¾hh wdrïN lrkak ^Tfí mdvu wdÈh&;
ixúOdkh lrkq msKsi f;dr;=re fidhkak" ,nd .kak" úYaf,aIKh lrkak ^ieis ie,iqï wdÈh&;
úl,am i,ld n,d ld¾hCIu f,i wm%ud§ l%shdud¾.hla .kak ^fnod .kak&; j.ùu ^ysñldß;ajh&
iy;sl lrkq jia" ,efnk m%;sM, wëCIKh lrkak" ;lafiare lrkak" uek n,kak'
b.ekaùfuys ksr; jk ish¨ u .=rejrekag" bf.k .ekSfï yd b.ekaùfï m%S;sh ,efíjd hs
m%d¾:kd lsÍug uu fuh wjia:djla lr .ksñ' fuu fmd; iïnkaOfhka jk Tfí ksÍlaIK yd
w;a±lSï ms<sn| j" cd;sl wOHdmk wdh;kfhys wod< wOHhkdxYfha m%Odkshdg ^wjYH úfgl
ug o msgm;la iys; j& ,shd tùug fkdmelsf<kak'
uydpd¾h .=Kmd, kdkdhlaldr" o¾YkY+Í ^ld,agka&
wOHlaI ckrd,a
cd;sl wOHdmk wdh;kh

III
fmrjok
.Ks; úIhud,dj u`.ska YsIHhka ;=< ixj¾Okh lsÍug wfmalaIs; yelshdj,ska oekqu yd
l=i,;dj" ikaksfõokh " iïnkaO;d oelau " fya;= oelaùu yd .eg¨ úi£u m%Odk fõ' ´kE u
wfhl=f.a idudkH Ôú;h ;=< ixj¾Okh lr.; hq;= yelshd f,i wm f.jk m%dfhda.sl Ôú;h
foi ne¨úg fuu yelshd ukdj meyeÈ,s fõ' th tfia jqj o oYl .Kkdjla ;siafia .Ks;h úIh
YsIH idOk uÜgu by< kexùu i|yd úúO l%fudamdhka Ndú; l< o YsIH idOk uÜgu 50]
m%udKhla jgd jk nj w'fmd'i ^id'fm<& m%;sM, fmkakqï lrhs' tfiau Wiia fm< yeoEÍu i|yd
o .Ks;h w;HjYH fõ '
by; lreKq foi úuis,su;aj ne,Sfï § .Ks;h úIh YsIH idOk uÜgï by< kexùu i|yd
oekg Ndú; l%fudamdhka m%udKj;a fkdjk nj cd;sl wOHdmk wdh;kfha .Ks; fomd¾;fïka;=fõ
ye`.Suhs' fï i|yd úl,am úi÷ula f,i wkdjrK mÍlaIK ms<sn|j wjOdkh fhduq fldg we;'
.Ks; úIfha ish¨u ixl,am wjfndaOh i|yd ixl,am w;r ;sria yd isria ifudaOdkh ms<sn| j
oekSu wjYH fõ' tfukau iEu ixl,amhla u ir, nfõ isg ixlS¾K nj olajd wjfndaOh wjYH
fõ' tu ksid tla tla YsIHhd tla .Ks; ixl,amhl okakd uÜgu wjfndaO lr f.k t;eka isg
ixl,amh bf.kSug Tjqkag wjia:dj ,nd §u iEu .=rejrfhl=f.a u j.lSuls' tneúka .=rejrhdg
YsIH yelshd iy fkdyelshd fyd¢ka yqkd .ekSug yelsjk mßÈ tla tla f;audj, wka;¾.;h
iqúfYaIs mshjr .Kkdjlg fnod we;' tu iEu mshjrl § u isiqka ,nd .; hq;= oekqï y÷kd .ekSug
iqÿiq m%Yak YsIHhkaag .e<fmk f,i ilia lr we;' fuu.ska .=rejrhdg YsIHhkaf.a yelshd iy
fkdyelshd iy tla tla YsIHhdf.a oekqu uÜgu yqkd .ekSug yels fõ'
.=rejrhd fuu WmlrK ms<sn| j wjfndaO lr f.k YsIHhdg .e<fmk m%Yak ldKav ,nd §u
u`.ska .=rejrhdf.a ld¾hhg;a YsIHhkaag;a myiq jkq we;'
fuu WmlrKj, m%dfhda.sl nj iy j,x.= nj y÷kd .ekSug w;ayod ne,Sï o isÿ lr we;' fuu
WmlrK YsIHhkaaf.a .Ks; oekqu l%ñl j j¾Okh lsÍug WmldÍ jkq we;' fuu i;a ls%hdj
lsÍu i|yd odhl jQ cd;sl wOHdmk wdh;kfha jHdmD;s lKavdhug;a ndysr iïm;a mqoa., odhl;aj
oela jq ieug;a w;ayod ne,Sï i|yd odhl jq ieug;a tfuka u fiiq ld¾hj, § iydh jQ ieug;a
ia;=;s lrñ'
fla'wd¾'m;auisß
wOHlaI

IV
ye¢kaùu
.Ks;h ixl,amuh úIhla nj wOHdmk{hska f.a u;h hs' .Ks;h bf.kSfï § .Ks;uh
ixl,am f.dvke.Su isÿjkafka wkql%uhla" ms<sfj<la" wkqj fõ' uQ,sl ixl,am .%yKh fkdùfuka
miqld,Sk j oaú;Shsl ixl,am .%yKh lr .ekSug ÿIalr fõ' bka Ydia;S%h lghq;=j, W!k idOkhla
we;s fõ' W!k idOkh fya;=fjka wOHdmkh ms<sn| j we;s wdYdj ySk ù bf.kqfuka bj;aùug yd
NS;shla we;s lr .ekSug fm,fò' fuu ;;a;ajh wm rfÜ orejkaf.a .Ks; wOHdmkh yd Rcq f,i
u ne£ mj;akd nj ie,lsh yels h'
wkdjrK mÍlaIK hkq fudkjd o @
YsIHhkaa ;=< ;sfnk hï hï ÿ¾j,;d wkdjrKh lr .ekSfï wruqKska meje;afjk mÍlaIK
wkdjrK mÍlaIK kñka ye¢kafõ' uQ,sl l=i,;d W!k;dj b.ekaùfï jevms<sfj<la wdrïNfha §
u y÷kd .ekSu wjYH h' wkdjrK mÍlaIK ilia lrkqfha fujeks W!k;d y÷kd .ekSfï woyiska
h' ^idOk mÍlaIK - 16 msgqj& wkdjrK mÍlaIKhl ld¾hh jkqfha hï iqúfYaI wOHhk lafIa;%hla
fyda úIh lreKla wdYs%;j YsIHhd fmkakqï lrk iqúfYaIs ÿ¾j,;d yd olaI;d fidhd .ekSu hs'
^ Introduction to Educational Measurment - page 445& ´kE u nqoaêu;a b.ekaùï ls%hdj,shl yd
M,odhs ud¾f.damfoaYhl moku wkdjrKh fõ' ( Practice of Educational Measurment - page 220 )
.=rejrhdf.a m%Odk N+ñldj jkafka YsIHhkaa w;r .=Kd;aul bf.kqï ls%hdj,shla we;s lr,Su hs'
fuh l< yels jkafka YsIHhka ls%hdldÍj bf.kqï ls%hdj,shg iyNd.s jkafka kï muKs'
bf.kqï,dNshd bf.kqï b.ekaùï ls%hdj,sfha § isÿlrkq ,nk jerÈ y÷kd .ekSu wjYH fõ' fuu
mshjf¾ § .=rejrhdf.a ld¾h ffjoHjrfhl=f.a ld¾h yd iudk h' ffjoHjrhd frda.shdf.a frda.h
yqkd .ekSu i|yd úúO mÍlaIK isÿ lr" frda.h wkdjrKh lrf.k" ta i|yd kshñ; m%;sldr
,nd foa' wOHdmkfha § wkdjrK mÍlaIK o yeisfrkafka frda.h y÷kd .ekSu i|yd ffjoHjrhd
fhdod .;a mÍlaIKj,g iudk whqßks'
wkdjrK mÍlaIK mka;s ldurfha flfia Ndú; lrkafka o @
kshñ; úIh tallhla fyda ud;Dldjla iïmq¾K lsÍfuka wk;=re j YsIHhkaf.a idOk uÜgu
mÍlaIKhla u.ska ;lafiare lsÍu isÿ flf¾' fuu ;lafiarefjka YsIHhka ms<sn| j hï hï
ks.ukj,g t<öug yels fõ' we;eï YsIHhkaa wfmalaIs; idOk uÜgu fmkakqï lrk w;r we;eï
YsIHhka wfmalaIs; idOk uÜgï lrd t<ö fkdue;s nj ;yjqre lr .; yels fõ' oeka fuu
wfmalaIs; idOk uÜgug <Õd ù fkdue;s fifuka bf.k .kakd YsIHhkag ta i|yd n,mE fya;=
fudkjd oe hs úuid ne,sh hq;= fõ' fï i|yd úúO fya;= mej;sh yels h' úfYaIfhka u fodaI
fmkakqï lr we;s ÿIalr lafIa;% yd ixl,am fidhd .ekSu w;HjYH fõ' fuf,i bf.kqï ÿIalr;d
mj;akd lafIa;% y÷kdf.k Bg fya;= úksYaph lsÍu i|yd wkdjrK mÍlaIK fhdod .; hq;= fõ'
bf.kqï ÿIalr;d mj;akd lafIa;% y÷kd .ekSfuka miq j YsIHhka fyd¢ka m%;spdr fkdoelaùug
fya;= fidhd .; hq;= fõ' tys § .=rejrhdf.a ld¾hNdrh frda. úksYapfha fhfok ffjoHjrfhl=f.a
ld¾hNdrhg iudk fõ' wOHdmk ls%hdj,sh ;=< fuu ;;a;ajh i|yd fhdod .kakd l%uh wkdjrK
mÍlaIK f,i yeÈkafõ' idudkH we.hSul § YsIHhkaf.a idOkh ;lafiare flrk ^assess) w;r"
wkdjrK mrSlaIKhl oS YsIHhkaaf.a yelshd úYaf,aIKh ( analysis ) flf¾'
wkdjrK mÍlaIKhl § my; oelafjk mshjr ms<sn| j wjOdkh l< hq;= fõ'
i Woõ wjYH YsIHfhda ljryq o @

V
ii fodaI iys; úIh lafIa;% $ ixl,am fudkjd o @
iii fuu fodaI we;s ù ;sfnkafka l=ula ksid o@
by; lreKq mokï lr f.k .Ks;h i|yd 6-9 fY%aKs úIh wka;¾.;hg wod<j wkdjrK
mÍlaIK lÜg, myla cd;sl wOHdmk wdh;kfha .Ks; fomd¾;fïka;=j úiska ilia lrk ,§'
wvq idOk uÜgï fmkakqï lrk bf.kqï ÿIalr;d iys; úIh laafIa;% y÷kd .ekSfuka miqj
bf.kqï ÿIalr;dj,g fya;= úuid ne,Su i|yd fuu wkdjrK mÍlaIK Ndú; l< yels fõ' tla
tla wkdjrK mÍlaIKh mehl muK ld,hlska ksu l< yels mßÈ ilia lr we;'
wkdjrK mrslaIK ieliSfï § wkq.ukh lrk ,o mshjr
1' m%Odk tallh jvd iqúfYaI f,i Wm tallj,g fnod .ekSu'
2' iqúfYaI m%Yak fY%aKshla ,ehsia;=.; lsÍu'
tu tla tla m%Yakh tla iqúfYaI lreKla muKla mÍlaId lsÍu i|yd ilia lr we;'
3' tla tla m%Yakh i|yd tl u j¾.fha ksoiqka ;=kla fyda Bg jeä ixLHdjla bÈßm;a lr
we;'
thska wkdjrK mÍlaIKfha j,x.= nj by< uÜgul mj;ajd .ekSu wfmalaId flf¾'
wkdjrK mÍlaIKj, wka;¾.;h
iEu ud;Dldjla hgf;a jQ wkdjrK mÍlaIKj, my; oelafjk uq,sldx. wka;¾.; lr we;'
1' ld¾h úYaf,aIKh
m%Odk tall" Wm tall yd iqúfYaI wruqKq yd tla tla wruqKg wod< m%Yak wxlh
we;=<;a lr we;'
2' wkdjrK mÍlaIK m%Yak m;%h
tla m%Yak m;%hla mehl ld,hl§ wjika l< yels mßÈ ilia lr we;'
3' ms<s;=re yd Wmfoia'
YsIHhka ms<s;=re iemhSfï § ms<s;=rej, wka;¾.; úh hq;= úfYaI lreKq yd uÜgï
Wmfoia hgf;a we;=<;a lr we;'
fuu fmdf;ys wka;¾.;h
fuu fmdf;ys wka;¾.; jkafka ixLHd hk f;audj hgf;a ieliQ wkdjrK mÍlaIK fõ'
uQ,sl .Ks; l¾u hgf;a m%Yak m;% y;rla o ixLHd rgd hgf;a m%Yak m;% tlla o Nd. hgf;a m%Yak
m;% ;=kla o oYu hgf;a m%Yak m;% ;=kla o" wkqmd; hgf;a m%Yak m;% ;=kla o" m%;sY; hgf;a m%Yak
m;% ;=kla o" j¾.M,h hgf;a m%Yak m;% tlla o f,i wkdjrK mÍlaIK 17la fuys wvx.= fõ'
.Ks; yelshd we.hSfï § ie,lsh hq;= idOl
1' ksrjoH;dj
2' m%;spdr fõ.h
3' ixj¾Ok uÜgu
4' .=Kd;aulNdjh
5' w;aoelSï lafIa;%h ^yelshd mrdih&
7' Ñka;k l%uh yd ld¾h idOkh

VI
fuu wkdjrK mÍlaIK Ndú;h i|yd Wmfoia
1' wkdjrK mÍlaIKh ,nd Èh hq;= YsIHhka y÷kd .kak'
2' bf.kqï ÿIalr;d fmkakqï lrk lafIa;% y÷kd .kak'
3' wkdjrK mÍlaIK meje;aùu i|yd fhda.H fõ,djla f;dard .kak'
4' iEu m%Yak m;%hl u m<uqjk m%Yakfha isg mshjfrka mshjr W;a;r iemhSug YsIHhkaag Wmfoia
fokak'
5' fuu mÍlaIKfha jeo.;alu YsIHhkaag wjfndaO lrjkak' tu.ska W;a;r iemhSfï § idlÉPd
lsÍu fyda fldms lsÍu j<lajd .kak'
6' tla m%Yak m;%hla i|yd mehl muK ld,hla jeh fj;e hs wfmalaId flf¾'
7' YsIHhkaaf.a W;a;r m;% ,l=Kq lsÍfï § W;a;r iu. § we;s Wmfoia ms<sm¢kak'
8' hï m%Yak wxlhla hgf;a f.dkq lr we;s whs;u ish,a,g u ksjerÈ W;a;r ,nd § we;akï
muKla tu úIh lreKg wod< m%ùK;d uÜgug YsIHhd ,`.dù we;ehs i,lkak'
m%Yak m;%fha wvx.= iudka;r m%Yak ;=fkka tlla ksjerÈ kï th wyUq f,i isÿjQjla f,i
i,lkak'
9' W;a;r m;% ,l=Kq lsÍfï § .Kas; yelshd we.hSfï § ie,lsh hq;= idOl ms<sn| j ie,ls,su;a
jkak' ^ksrjoH;dj" m%;spdr fõ.h" ixj¾Ok uÜgu" .=Kd;aulNdjh" w;aoelSï lafIa;%h"
ld¾h idOkh &
10' wkdjrK mÍlaIKfhka bf.kqï ÿIalr;djg fya;= jq lreKq y÷kdf.k iqÿiq m%;sld¾h jev
ie,iqï lr ls%hd;aul lrkak'
m%;SldÍ jev ie,iqïlsÍfï § ie,lsh hq;= idOl
i. W;a;r m;% ,l=Kq lr ,l=Kq úYaf,aIKfhka YsIHhkaaf.a bf.kqï ÿIalr;d i|yd fya;=
ù we;s lreKq iqúfYaIj y÷kd .kak' tu lreKq ms<sn| j YsIHhka iu. iïuqL
idlÉPd mj;ajñka tu lreKq .eUqßka wOHhkh lrkak' yels;dla ÿrg flaj, iïuqL
idlÉPd mj;ajkak'
ii. fifuka bf.kSug fya;= jq wkshï idOl .fõIKh lrkak' m%udKj;a ;rï mqreÿ
fkdùu" mdi,a fkdmeñKSu " wikSm yd fi!LH ;;a;ajh " jerÈ mqreÿ ms<sn| ie,ls,su;a
jkak'
iii. YsIHhkaaf.a ksrjoH;dj" .=Kd;aul Ndjh ms<sn|j ie,ls,su;a ù ta ms<sn| j YsIHhkag
Wmfoia fokak'
iv. fifuka bf.k .kakd YsIHhkaaf.a fõ.h jeä lr,Su i|yd kej; kej; wNHdifha
ksr; lrjkak'
v. m%;SldÍ jev ie,iqï lsÍfï § foaYk l%uh yels;dla ÿrg neyer lrkak' lKavdhï
ls%hdldrlï" úfkdao ckl lS%vd jeks oE yels;dla ÿrg ie,iqï lrñka b.ekaùï
ls%hdj,sh fufyh jkak'
vi. YsIHhka w;r M,odhS idlÉPd yd wka;¾ ls%hd isÿ jk wdldrhg bf.kqï - b.ekaùï
ls%hdj,sh ie,eiqï lrkak'
vii. úhqla; ixl,am yels;dla ÿrg ixhqla; w;aoelSï weiqßka ;yjqre lrkak'
viii. m%;SldÍ bf.kqï ls%hdj,sh i|yd ksjerÈ yd iqÿiq bf.kqï øjH Ndú; lrkak'
ix. YsIHhkaf.a m%.;sh ms<sn| j l%udkql+, j jd¾;d ;nd .kak'
x. YsIHhkaf.a bf.kqï fodaI j<lajd Tjqka wod< úIh ks¾foaYfha úIh lreKq flfrys
fhduq lrjkak'

VII
wkdjrKh u.ska jeä ÈhqKq jQ .=Kd;aul bf.kqula fmkakqï lrk
wkql%uh'
bf.kqu - b.ekaùu we.hSu YsIHhkaf.a wi;=gqodhl wkdjrKh i|yd
ld¾h idOkh wjia:dj
wkdjrK mÍlaIK ÿIalr lafIa;% Woõ wjYH YsIHhka idudkH idOk mÍlaIKhla
u`.ska bf.kqï msysgqjd .ekSu y÷kd .ekSu meje;aùu fyda fmr meje;a
ÿIalr;djg fya;= jQ mÍlaIKj, o;a;
y÷kd .ekSu
by; wkql%ufha mßÈ YsIHhkaa fodaI yd ÿIalr;d fmkakqï lrk lafIa;% i|yd wkdjrK mÍlaIK
f.dvkxjd YsIH yelshd úYaf,aIKh l< yels fõ' wm ilia lr we;s úIh lafIa;%hg wu;rj
wfkla úIh lafIa;% w<,d wkdjrK mÍlaIK ;ekSug Wkkaÿ jkak' wm ilid we;s wkdjrK
mÍlaIK ms<sn| j ixj¾Okd;aul fhdackd wm fj; okajd tjkafka kï fnfyúka lD;{ fjuq'
.Ks;h wiu;a j Wiia wOHdmk wjia:d wysñ lr .kakd ,laI ixLHd; YS% ,dxlsl orejka
fjkqfjka fuu wkdjrK mÍlaIK ie,iqï lr we;' fïjd ls%hd;aul lr oefha orejkaf.a keKei
Tma kexùug yelsfõjd hkak wmf.a m%d¾:kh hs '
Ô't,a' lreKdr;ak
fcHIaG wOHdmk{
jHdmD;s lKavdhï kdhl'
m%;SldÍ jev
l%shd;aul lsÍu
jeäÈhqKq jQ
.=Kd;aul bf.kqu

VIII
m%;SldÍ b.ekaùu
mka;s ldurh ;=< isák fndfyda YsIHhka úúO bf.kqï ÿIalr;dj,ska hqla; h' ta w;r u;lfha
wvq nj" bf.kqu i|yd wNsfm%arKh ùfï ÿ¾j,;d" wjOdkh fhduq ùfï ÿ¾j,;d" .eg¨ úi§fï
yelshdfõ ÿ¾j,;d" úúO ixl,am .%yKh lr .ekSfï ÿ¾j,;d iy wod< wjia:dj, § W.;a oekqu
ksjerÈ f,i Ndú; lsÍfï ÿ¾j,;d i|yka l< yels h'
YsIHhka ;=< úúO jQ bf.kqï ÿIalr;d olakg ,efnk w;r u úúO jQ yelshd fukau úúO
bf.kqï l%u o Tjqka i;=j mj;S' iuyr YsIHhka oDYH udOHfhka bf.kSug jvd olaI w;r iuyr
wh Y%jH udOHfhka bf.kqug jvd ksmqK;ajhla olajhs' tfia u ;j;a iuyr YsIHhkaa m%dfhda.sl
w;aoelSï ;=,ska bf.kSug ms%h lrhs'
fï wkqj Tjqka ;=< mj;akd yelshd fuka u bf.kqï l%u o ie,ls,a,g .ksñka Tjqka ;=<
mj;akd bf.kqï ÿIalr;d wju lsÍu wruqK lr .ksñka Tjqkaf.a bf.kqï mßirh ;=< Tjqkag iqÿiq
ksjerÈ b.ekaùfï yd bf.kqï øjH fhdod .ksñka Tjqkaf.a bf.kqfuys .=Kd;aul nj by< kexùu"
"m%;SldÍ b.ekaùfuka wfmalaId flf¾' m%;SldÍ bf.kqfuys wdrïNh jkafka wkdjrK mÍlaIKhlska
.kakd f;dr;=re h '
YsIHhkaf.a bf.kqï ÿIalr;d wju lsÍfï wruqKska isÿ lrkakd jq m%;SldÍ b.ekaùfuys §
ie,ls,su;a úh hq;= lreKq rdYshls' tajd w;r .=re iQodku " úúO bf.kqï ls%hdldrlï Ndú;h" iqÿiq
bf.kqï wjia:d ixúOdkh " b.ekaùfï l%fudamdhhka" meyeÈ,s f;dr;=re iemhSu" m%Odk lreKq
idrdxY .; lsÍu" bf.kqï leue;a; yd wNsfm%arKh by< kexùu" mka;s ldur ls%hdldrlï i|yd
YsIHhkaf.a ls%hdldÍ iyNd.s;ajh by< kexùu bf.kqï ls%hdj,sh flfrys wjOdrKh lsÍu iy tla
tla YsIHhkaf.a yelshd ms<sn| ie,ls,a,g .ekSu fõ'
fuu lreKq ms<sn| j iúia;rd;aulj úuid n,uq'
.=re iQodku
mdvï ms<sfh, lsÍug fmr " m%;SldÍ b.ekaùï isÿlrk .=rejrhd úiska YsIHhkaf.a bf.kqï
ÿIalr;d yels blaukska y÷kd.; hq;= h' ta i|yd wkdjrK mÍlaIKhla Ndú; l< hq;= fõ' thg
wkqj YsIHhdg jvd;a M,odhs b.ekaùfï ie,iqula ilia lr .; hq;= fõ' tu W.;a m%Odk lreKq
jdÑl j fyda ,sÅ; j fyda mka;s ldurh fj; bÈßm;a lsÍug fhduq l< yels h' tu.ska Tyqf.a
u;lh ;j ÿrg;A ;yjqre l< yels fõ'
bf.kqï leue;a; iy wNsfm%arKh by< kexùu
mka;s ldur bf.kqï wjia:dj, § bf.kqï ÿIalr;d fya;=fjka l%u l%ufhka bf.kSu
i|yd Tjqkaf.a we;s leue;a; iy wdYdj wvqfõ' tneúka .=rejrhd úiska úIhud,dj" YsIHhkaf.a
wjYH;d iu. iïnkaO lr .; hq;= hs' YsIHhkaaf.a leue;a; o ie,ls,a,g .ksñka .=rejrhd úiska
rij;a ls%hdldrlï ie,iqï lsÍu jvd;a M,odhS fõ'
mka;s ldur ls%hdldrlï i|yd YsIHhkaaf.a ls%hdldÍ iyNd.s;ajh by< kexùu
bf.kqï ÿIalr;d iys; YsIHfhda fndfyda úg iajhx wOHhkhl fh§ug ÿ¾j, tfia u ;rula
ksyX wh fj;s' Tjqyq m%Yak weiSug fyda Tjqkaf.a woyia bÈßm;a lsÍug ue,sfj;s' tneúka .=rejrhd
tu YsIHhkaa ls%hdldÍ iyNd.s;ajh i|yd ffO¾hu;a l< hq;= fõ'

IX
bf.kqï ls%hdj,sh flfrys wjOdrKh lsÍu
b.ekaùu" oekqu iïfm%aIKh lsÍu i|yd muKla wjOdrKh lsÍu iqÿiq fkdfõ' bf.kqï ls%hdj,sh
u.ska YsIHhkag M,odhs ld¾hhla isÿ jkafka oe hs fidhd ne,sh hq;= fõ' tfia u YsIHhka úiska
Tjqka W.;a foa ms<sn| is;Sug iy m%dfhda.slj w;ayod ne,Sug;a" .eg¨ úi§u i|yd;a wjia:d Wodlr
Èh hq;= fõ' tfiau .=rejrhd úiska tu wjia:d mßiaifuka ksrSlaIKh l< hq;= w;r Tjqkaf.a
l=i,;d wkqj Tjqkag wjYH iyfhda.h iy m%;sfmdaIKh ,nd Èh hq;= h' tu.ska Tjqka ffO¾hu;a
l< hq;= fõ'
úúO bf.kqï ls%hdldrlï Ndú;h
YsIHhka ;=< úúO bf.kqï ,laIK fmkakqï lrk neúka .=rejrhd úiska úúO bf.kqï ls%hdldrlï
ixúOdkh lr .; hq;= fõ' fï wkqj Tjqka ;=< mj;akd úúO yelshd yd l=i,;d fuu.ska ixj¾Okh
l< yels fõ' fuys§ jvd;a M,odhs jkafka tla §¾> ls%hdldrlula ixúOdkh lsÍu fkdj wod< ir,
ls%hdldrlï fY%aKshla uÕska YsIHhkag wjYH oekqu yd l=i,;d ,nd §u hs'
iqÿiq bf.kqï wjia:d ixúOdkh
m%;SldÍ b.ekaùfuys fhfok .=rejrhd úiska iqÿiq bf.kqï wjia:d ixúOdkh lr .; hq;= h'
ksoiqkla f,i bx.S%is NdIdj i|yd NdId mßirhla f.dvke.Su fyda .Ks;h úIh i|yd l%Svd
ixúOdkh i|yka l< yels h'
b.ekaùfï l%fudamdhhka
.=rejrhd úiska úhqla; ixl,am meyeÈ,s lsÍfï §" YsIHhkaf.a bf.kqï yelshd wkqj ixhqla;
WodyrK Ndú; lrñka ir, mshjr Tiafia th isÿ l< hq;= h' .=rejrhd úiska YsIHhkaf.a ls%hdldÍ
iyNd.s;ajh we;s lsÍu i|yd wjYH ;rï bf.kqï wdOdrl Ndú;h yd l%Svd iy ls%hdldrlï Ndú;d
lsÍu jeo.;a h' tfiau m%Odk lreKq meyeÈ,s lsÍfï § f;dr;=re ;dlaIKh iy Ndú; l< yels ish¿
iïm;a Ndú;fhka YsIHhkag myiqfjka lreKq wjOdrKh l< yels fõ'
meyeÈ,s f;dr;=re iemhSu
bf.kqï ÿIalr;d iys; fndfyda YsIHhkaf.a ,sÅ; NdIdj wjfndaO lr .ekSfï l=i,;dj wju
uÜgul mj;S' tneúka .=rejrhd úiska ir, iy meyeÈ,s f;dr;=re iemhSfuka YsIHhkaf.a jerÈ
jgyd .ekSï u.yrjd .; yels h' tfiau bf.kqï ls%hdldrlï ys mshjr ir, j meyeÈ,s l< hq;= fõ'
yelskï YsIH wjYH;dj u; tu ls%hdldrlï ys mshjr kej; kej;;a meyeÈ,s lsÍu jvd;a M,odhs
fõ'
m%Odk lreKq idrdxY .; lsÍu
mdvu wjidkfha .=rejrhd úiska tu mdvug wod< m%Odk lreKq kej; isysm;a l< hq;= w;r tu
lreKq l¿,E,a, u; i|yka l< hq;= fõ' tu.ska " Y%jH yd oDIH udOH u.ska W.;a úIh lreKq
kej; isysm;a l< yels fõ' tfia u tÈfkod Ôú; w;aoelSï iu. W.;a úIh lreKq iïnkaO lr
.ekSu i|yd YsIHhka fhduq l< hq;= fõ '
Ô' mS' tÉ' c.;a l=udr
fcHIaG lÓldpd¾h
cd;sl wOHdmk wdh;kh

X
WmfoaYkh (
uydpd¾h .=Kmd, kdkdhlaldr
wOHlaI ckrd,a
cd;sl wOHdmk wdh;kh
tï¡ t*a¡ tia¡ mS¡ chj¾Ok
ksfhdacH wOHlaI ckrd,a
úoHd yd ;dlaIK mSGh
cd;sl wOHdmk wdh;kh
wëlaIKh(
fla¡ rxð;a m;auisß
wOHlaI
cd;sl wOHdmk wdh;kh
ie,iqu yd iïnkaëlrKh(
Ô¡ t,a¡ lreKdr;ak
fcHIaG wOHdmk{
wOHdmk fmdÿ iy;sl m;%^id'fm<& m%;sM, by< kxjd,Sfï jHdmD;sfha lKavdhï kdhl'
cd;sl wOHdmk wdh;kh
fou< udOHh iïnkaëlrKh(
tia' rdfÊkaøï uhd
lÓldpd¾h
cd;sl wOHdmk wdh;kh
6 - 9 fY%aKs úIh wka;¾.;hg wod< j ilia lr we;'

XI
ndysr iïm;a odhl;ajh (
tÉ'tï'ta'chfiak uhd úY%dñl .=re WmfoaYl
jhs'ù'wd¾'ú;dru uhd .=re WmfoaYl
l,dm wOHdmk ld¾hd,h" foyss´úg
tka'Ô'fifkúr;ak uhd .=re WmfoaYl
chïm;a f,dl=uqo,s uhd .=re fiajh
ckdêm;s úoHd,h" uyr.u
Ô'tÉ'tia'rxckS o is,ajd ñh .=re fiajh
O¾umd, úoHd,h" mkaksmsáh
ã't,a' ngq.yf.a uhd úY%dñl mSGdêm;s
ishkE cd;sl wOHdmk úoHdmSGh" fõhkaf.dv
mß.Kl msgq ieliqu( wd¾'mS'ã'iS' chisxy uhd
.=re WmfoaYl
NdIdj ixialrKh ( tÉ¡ mS¡ iqis,a issßfiak uhd
lÓldpd¾h
ydmsá.u cd;sl wOHdmk úoHdmSGh
msg ljr ks¾udKh ( cd;sl wOHdmk wdh;kh
iydh ld¾h uKav,h ( tia' fyÜáwdrÉÑ"
.Ks; fomd¾;fïka;=j"
cd;sl wOHdmk wdh;kh'
fla' fk,sld fiakdks"
wd¾' tï' rEmisxy"

XII
mgqk
msgqj
1' mßñ;sh - i
1'1' ld¾h úYaf,aIKh i 01
1'2 wkdjrK mÍlaIK m;%h i 03
1'3 W;a;r yd Wmfoia i 09
2' mßñ;sh - ii
2'1 ld¾h úYaf,aIKh ii 10
2'2 wkdjrK mÍlaIK m;%h ii 13
2'3 W;a;r yd Wmfoia ii 21
3' j¾.M,h - i
3'1 ld¾h úYaf,aIKh i 22
3'2 wkdjrK mÍlaIK m;%h i 24
3'3 W;a;r yd Wmfoia i 31
4' j¾.M,h - ii
4'1 ld¾h úYaf,aIKh ii 34
4'2 wkdjrK mÍlaIK m;%h ii 37
4'3 W;a;r yd Wmfoia ii 46
5' mßudj
5'1 ld¾h úYaf,aIKh 48
5'2 wkdjrK mÍlaIK m;%h 51
5'3 W;a;r yd Wmfoia 62
6' jD;a;hl j¾.M,h
6'1 ld¾h úYaf,aIKh 65
6'2 wkdjrK mÍlaIK m;%h 67
6'3 W;a;r yd Wmfoia 74

.Ks; fomd¾;fïka;=j cd;sl wOHdmk wdh;kh1
wkdjrK mÍlaIK ñkqï
mßñ;sh - I
ld¾h úYaf,aIKh
1'1 È. ms<sn| ixl,amh
1'2 È. uksk tall'

1' mßñ;sh
wkdjrK mÍlaIKh -
iúia;rd;aul ld¾h úYaf,aIKh
m%Yak wruqKq wruqKq
wxlh wxlh
1'1 È. ms<sn| ixl,amh
1 1'1'1 § we;s rEm w;=ßka Èf.ka jeä rEmh f;darhs'
2' 1'1'2 § we;s rEmhl kï lrk ,o m<, È.la f,i y÷kd .kshs'
3' 1'1'3 § we;s rEmhl kï lrk ,o Wi È.la f,i y÷kd .kshs'
4' 1'1'4 § we;s rEmhl olajd we;s .eUqr È.la f,i y÷kd .kshs'
5' 1'1'5 rEmhl olajd we;s >klu È.la f,i y÷kd .kshs'
6' 1'1'6 m<, " Wi " .eUqr " >klu hkq È.la f,i y÷kd .kshs'
1'2 È. uksk tall
7"8 1'2'1 È. uksk tall y÷kd .kshs'
9 1'2'2 ñ,sógrj,ska § we;s È. m%udK folla tl;= lrhs'
10 1'2'3 ñ,sógrj,ska § we;s È. m%udK folla wvq lrhs'
11 1'2'4 fikaáógrj,ska § we;s È. m%udK folla tl;= lrhs'
12 1'2'5 fikaáógrj,ska § we;s È. m%udK folla wvq lrhs'
13 1'2'6 fikaáógrj,ska § we;s È. m%udKhka ñ,sógrj,ska olajhs'
14 1'2'7 ñ,sógrj,ska § we;s È. m%udKhka fikaásógrj,ska olajhs'
15 1'2'8 fikaáógr yd ñ,sógrj,ska § we;s È. m%udK folla tl;= lrhs'
16 1'2'9 ñ,sógr yd fikaáógrj,ska § we;s È. m%udK folla wvq lrhs'
17 1'2'10 ógrj,ska § we;s we;s È. m%udK folla tl;= lrhs'
18 1'2'11 ógrj,ska § we;s we;s È. m%udK folla wvq lrhs'
19 1'2'12 ógrj,ska § we;s È. m%udK fikaá ógr njg mßj¾;kh lrhs'
20 1'2'13 oYu ia:dk 1 la iys; j ógrj,ska ±lafjk È. m%udKhka"
fikaáógrj,g mßj¾;kh lrhs'
21 1'2'14 oYu ia:dk 2 la iys; j ógrj,ska ±lafjk È. m%udKhka"
fikaáógrj,g mßj¾;kh lrhs'
22 1'2'15 W;a;r mQ¾K ixLHdjla jkfia fikaáógrj,ska ±lafjk È.
m%udKhka" ógrj,ska olajhs'
23 1'2'16 W;a;r oYu ia:dk tlla jkfia fikaáógrj,ska ±lafjk È.
W;a;r oYu ia:dk folla jkfia fikaáógrj,ska ±lafjk È.
m%udKhka" ógrj,ska olajhs'
25 1'2'18 ógr yd fikaásógrj,ska § we;s È. m%udK folla tl;= lrhs'
26 1'2'19 ógr yd fikaáógrj,ska § we;s È. m%udK folla wvq lrhs'
I

mßñ;sh I
wkdjrK mÍlaIKh - 1
m%Yak m;%h'
m%Yak ish,a,gu W;a;r imhkak'
1' my; tla tla rEm w;=ßka È.ska jeä rEmh f;dard Bg ysñ wlaIrh ysia;ek u;
,shkak '
(i) (ii) (iii)
''''''''''''''''''''' ''''''''''''''''''''' '''''''''''''''''''
2' w¢k ,o rEmhg wkqj § we;s m%ldYh ksjerÈ kï ,l=K o" jerÈ kï ,l=K o
" Bg bÈßfhka we;s fldgqj ;=< fhdokak'
a. a.
a.
b. b.
b.
 
(i)
(ii)
(iii)
5 cm
5 cm
4 cm
2 cm
4 cm
4 cm 4 cm
4 cm
2 cm
fuu RcqfldaKdi%fha hkq os.la fõ'2 cm
fuu >kldNfha hkq os.la fkdfõ'4 cm
fuu iup;=ri%fha mdohl È. fõ'4 cm

3'
(i)
(ii)
(iii)
fuu rEmfhka ±lafjkafka Wi jQ
Wux fodrls' fuys u.ska ±lafjkafka È.ls '
5 m
5 m
fuu úÿ,s myka lKqfõ Wi fõ'
fuu Wi" È. f,i y÷kajhs '
8 m
fuu .fia Wi ls'
u`.ska ±lafjkafka È.la fkdfõ'
12 m
12 m
4'
15 m
(i)
(ii)
fuu <sf|a .eUqr ógr 15 ls' fuys
È.la fkdfõ '15 m
2 m
5 m
12 m
fuh la .eUqr fmdl=Kls' fuu .eUqr
È.la f,i ±laúh yels h '
2 m
8 m

(iii)
( i )
(ii )
(iii)
1 cm
6' fmÜáhl È." m<, " Wi hk ñkqï ;=k u È. fõ'
gexlshl .eUqr È.la fkdfõ '
´kE u ;yvqjl >klu hkq È.ls '
( i )
(ii )
(iii)
fuu c,dYfha .eUqr ls '
tys hkq È.ls'3 m
3 m3 m
5.
remsh,
1mm
fuh >klula we;s ;yvqjls'
tu >klu È.la f,i m%ldY l<
yels h '
1mm
,Sj,ska idod.;a yevhla fuys ±lafõ '
fuu ,S l=Üáfha >klu ls '
fuu hkq È.la fkdfõ '1 cm
1 cm
fuys ±lafjkafka remshf,a ldishls '
tys >klu jk
È.la fkdfõ '
2mm2mm

7' ksjeros jrKh f;dard háka brla woskak '
k.r folla w;r ÿr uekSug iqÿiq tallh jkafka"
h' h' h'
ldishl >klu uekSug iqÿiq tallh jkafka "
h' h' h'
.il Wi uekSug jvd;a iqÿiq tallhla jkafka "
h' h' h'
8'
os. uksk tallhla fkdjkafka "
h' h' h'
Wi uksk tallhla fkdjkafka "
h' h' h'
>klu uksk tallhla fkdjkafka "
h' h' h'
9' tl;= lrkak '
10' wvq lrkak '
11' tl;= lrkak '
12' wvq lrkak '
13' my; tall mßj¾;kh lrkak '
( i )
a ) km b ) kg c ) l
(ii)
a ) m b ) mm c ) km
(iii)
a ) g b ) l c ) m
(i)
a ) m b ) cm c ) g
(ii )
a ) mm b ) kg c ) m
(iii)
a ) ml b ) mm c ) cm
( i ) 13mm (ii ) 24mm (iii) 56mm
+ 17 mm + 6 mm + 49 mm
( i ) 57mm (ii ) 72mm (iii) 54mm
- 17 mm - 25 mm - 27 mm
( i ) 72 cm (ii ) 54 cm (iii) 45 cm
+ 93 cm + 27 cm + 59 cm
( i ) 72 cm (ii ) 52 cm (iii) 93 cm
- 28 cm - 37 cm - 46 cm
( i ) 5 cm = .............mm
(ii ) 7 cm = .............mm
(iii) 12 cm = .............mm

14' my; tall mßj¾;kh lrkak '
15' tl;= lrkak '
16' wvq lrkak '
17' tl;= lrkak '
18' wvq lrkak '
19' ógrj,ska § we;s È. m%udK fikaáógrj,g yrjd ,shkak '
20'
21'
22'fikaá ógrj,ska olajd we;s È. m%udK ógrj,g yrjd ,shkak'
( i ) 20mm = .............cm
(ii ) 50mm = .............cm
(iii) 70 mm = .............cm
( i ) cm mm (ii ) cm mm (iii) cm mm
3 7 4 7 1 9
+ 2 5 + 2 3 + 7 5
( i ) cm mm (ii ) cm mm (iii) cm mm
8 2 5 3 10 5
- 1 7 - 2 4 - 7 8
( i ) 427 m (ii ) 342 m (iii) 649 m
+ 538 m + 573 m + 249 m
( i ) 572 m (ii ) 721 m (iii) 824 m
- 193 m - 547 m - 172 m
( i ) 2 m = .............cm
(ii ) 5 m = .............cm
(iii) 7 m = .............cm
( i ) 2.5 m = .............cm
(ii ) 3.7 m = .............cm
(iii) 4.1 m = .............cm
( i ) 3.75 m = .............cm
(ii ) 1.24 m = .............cm
(iii) 3.25 m = .............cm
( i ) 300 cm = .............m
(ii ) 800 cm = .............m
(iii) 500 cm = .............m

23'
24'
25'tl;= lrkak'
26'wvq lrkak '
( i ) 870 cm = .............m
(ii ) 540 cm = .............m
(iii) 320 cm = .............m
( i ) 375 cm = .............m
(ii ) 584 cm = .............m
(iii) 727 cm = .............m
( i ) m cm (ii ) m cm (iii) m cm
5 24 7 45 3 77
+ 2 95 + 2 57 + 2 88
( i ) m cm (ii ) m cm (iii) m cm
7 45 12 25 10 55
- 3 24 - 9 70 - 4 70

wkdjrK mÍlaIKh - 1
W;a;r yd Wmfoia
m%Yak W;a;r Wmfoia
wxlh
1. ( i ) a (ii ) b (iii) b
2. ( i ) (ii ) (iii)
3. ( i ) (ii ) (iii)
4. ( i ) (ii ) (iii)
5. ( i ) (ii ) (iii)
6. ( i ) (ii ) (iii)
( i ) km (ii ) mm (iii) m
( i ) g (ii ) kg (iii) ml
( i ) 30mm (ii ) 30mm (iii) 105mm
( i ) 40mm (ii ) 47mm (iii) 27mm
( i ) 165 cm(ii ) 81 cm (iii) 104 cm
( i ) 44 cm (ii ) 15 cm (iii) 47 cm
( i ) 50 (ii ) 70 (iii) 120
( i ) 2 (ii ) 5 (iii)7
( i ) 6 2 (ii ) 7 0 (iii) 9 4
( i ) 6 5 (ii ) 2 9 (iii) 2 7
( i ) 965 m (ii ) 915 m (iii) 898 m
18. ( i ) 379 m (ii ) 174 m (iii) 652 m
19. ( i ) 200 (ii ) 500 (iii) 700
20. ( i ) 250 (ii ) 370 (iii) 410
21. ( i ) 375 (ii ) 124 (iii) 325
22. ( i ) 3 (ii ) 8 (iii) 5
23. ( i ) 8.7 (ii ) 5.4 (iii) 3.2
24. ( i ) 3.75 (ii ) 5.84 (iii) 7.27
25. ( i ) 8 19 (ii ) 10 02( iii ) 6 65
26. ( i ) 4 21 (ii ) 2 55 (iii) 5 85





7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
tall ,shd ;sìh hq;= hs'
tall ,shd ;sìh hq;= hs'

mßñ;sh - II
ld¾h úYaf,aIKh
1'3 ir, ;, rEmj, mßñ;sh'
1'4 ixhqla; ;, rEmj, mßñ;sh'
1'5 jD;a;hl mßêh

mßñ;sh II
wkdjrK mÍlaIKh
m%Yak wruqKq wruqKq
wxlh wxlh
1'3 ;, rEmj, mßñ;sh
1"2 1'3'1 mßñ;sh hk ixl,amh y÷kd. kshs'
3 1'3'2 mdo u; È. ,l=Kq l< ;%sfldaKhl mßñ;sh fidhhs'
4 1'3'3 tla mdohl È. ,l=Kq lr we;s iumdo ;%sfldaKhl mßñ;sh
fidhhs'
5 1'3'4 mdoj, os. ,l=Kq lr we;ss iuoaùmdo ;%sfldaKhl mßñ;sh fidhhs'
6"7"8"9 1'3'5 ;%sfldaKhl mdoj, os. ùÔh ixfla;j,ska § we;s úg tys mßñ;sh
ùÔh m%ldYkhlska olajhs '
10 1'3'6 iumdo ;%sfldaKhl mßñ;sh ÿka úg mdohl È. fidhhs'
11"12 1'3'7 iuoaùmdo ;%sfldaKhl mßñ;sh yd tla mdohla ÿka úg wfkla
mdoj, È. fidhhs '
13 1'3'8 iup;=ri%hl ish¨u mdoj, È. ,l=Kq lr we;s úg tysmßñ;sh
fidhhs '
14 1'3'9 iup;=ri%hl tla mdohl È. ,l=Kq lr we;s úg tu iup;=ri%fha
mßñ;sh fidhhs '
15"16 1'3'10 iup;=ri%hl mdohl È. ùÔh ixfla; j,ska § we;súg tys
mßñ;sh ùÔh m%ldYkhlska olajhs'
17 1'3'11 RcqfldaKdi%hl ish¨ mdoj, os. oS we;s úg tys mßñ;sh .Kkh
lrhs'
18 1'3'12 RcqfldaKdi%hl noaO mdo foll È. ,l=Kq lr we;s úg tys
mßñ;sh fidhhs'
19 1'3'13 mdoj, È. ùÔh ixfla;j,ska § we;súg RcqfldaKdi%fha
mßñ;sh i|yd m%ldYkhla f.dvk.hs'
20 1'3'14 RcqfldaKdi%hl mßñ;sh yd È. ÿka úg m<, fidhhs'
21 1'3'15 RcqfldaKdi%hl mßñ;sh yd m<, ÿka úg È. fidhhs'
1'4 ixhqla; ;, rEmhl mßñ;sh
22"23"24 1'4'1 § we;s ;, rEm w;ßka ixhqla; ;, rEm f;darhs'
25 1'4'2 ixhqla; ;, rEmhl ,laIK y÷kd .kshs'
26 1'4'3 ixhqla; ;, rEmhl mßñ;sh fidhhs'
27 1'4'4 ixhqla; ;, rEmfha mdo lSmhl È. yd wfkla mdoj, iïnkaO;d
,l=Kq lr § we;s úg rEmfha mßñ;sh fidhhs'
28 1'4'5 ixhqla; ;, rEmhl mdoj, È. ùÔh ixfla;j,ska § we;s úg
mßñ;sh i|yd ùÔh m%ldYkhla f.dvk.hs'
29 1'4'6 ixhqla; ;, rEmhl mßñ;sh .Kkh lrhs '

m%Yak wruqKq wruqKq
wxlh wxlh
1'5 jD;a;hl mßêh
30 1'5'1 jD;a;hl mßêh y÷kd .kshs'
31 1'5'2 jD;a;hl wrh kï lrhs '
32 1'5'3 jD;a;hl mßêh fiùu hgf;a ,efnk ixfla; y÷kd .kshs'
33 1'5'4 jD;a; ksh;fha wdikak w.h y÷kd .kshs'
34 1'5'5 jD;a;hl wrh ÿka úg mßêh .Kkh lrhs'
35 1'5'6 jD;a;hl úIalïNh ÿka úg mßêh .Kkh lrhs'

fuys ±lafjkafka bvul o<
rEmhls' tys jfÜ È. uek .;aúg
th tu bvfï mßñ;sh fõ'
( i )
(ii )
(iii)
( i )
(ii )
(iii)
( i )
....................... ...................... .....................
bvu
<ufhla fuu f.dvke.s,af,a
jfÜ È. uek Tyqg ,enqK È.
mßñ;shla fkdjk nj mjihs '

<ufhla fïi ,E,af,a jfÜ È.
uek.kS' ,enqKq uq¿ È.
mßñ;sh f,i lshhs'
5 cm
7 cm
5 cm5 cm
5 cm5 cm 3 cm
4 cm
5 cm
mßñ;sh II
wkdjrK mÍlaIKh
m%Yak m;%h
1' w¢k ,o rEmhg wkqj § we;s m%ldYh ksjerÈ kï ,l=K o" jerÈ kï
,l=K o " Bg bÈßfhka we;s fldgqj ;=< fhdokak'
2' ksjerÈ jrKh f;dard háka brla w¢kak'
´kEu ;, rEmhl jfÜ È. "
^ j¾.M,h fõ' $ mßñ;sh fõ' $ mßudj fõ' &
fuu RcqfldaKdi% wdia;rfha mßñ;sh hkq" tys
^ fl,ska È.hs' $ jfÜ È.hs' $ yria È.hs ' &
fuu ;%sfldaKdldr wdia;rfha udhsfï È. "
^ j¾.M,h fõ' $ mßudj fõ' $mßñ;sh fõ' &
3' my; olajd we;s ;%sfldaKj, " § we;s ñkqï wkqj mßñ;sh fidhkak'

(ii ) (iii) (iii)
4 cm
5 cm
10 cm
.................... ..................... ..................
(ii ) (iii) (iii)
..................... ..................... ..................
(ii ) (iii) (iii)
a a
a
p
p
p
m m
m
.................... ..................... ..................
(ii ) (iii) (iii)
a
b
c
qp
r
m n
q
..................... ..................... .....................
(ii ) (iii) (iii)
a
p
r
.......................... ........................ ...........................
4'
5'
6'
7'
8'
5 cm
3 cm
4 cm
6 cm
10 cm
5 cm

( i ) (ii ) (iii)
b a p
m
c
..................... ..................... ..................
( i ) ( ii ) (iii)
= 18 cm = 12 cm = 30 cm
= ........... = .......... = ..........
( i ) (ii ) (iii)
= 18 cm = 10 cm = 32 cm
x = ....... x = ........ x = .......
( i ) (ii) (iii)
= 40 cm = 50 cm = 30 cm
x = ....... x = ........ x = .......
9'
10' my; olajd we;s iumdo ;%sfldaKj, mrsñ;sh oS we;' tajdfha tla tla mdohl os.
fidhkak'
mrsñ;sh mßñ;sh mrsñ;sh
mdohl os. mdohl os. mdohl os.
11' my; olajd we;s iuoaùmdo ;%sfldaKj, mrsñ;sh oS we;' tajdfha tla tla mdohl x
u.ska oelafjk os. fidhkak'
12'
3 cm5 cm
x
5 cm
x
3 cm
x
10 cm 10 cm
x x x
8 cm10 cm 20 cm
r

( i ) ( ii ) ( iii )
( i ) ( ii ) ( iii )
4 cm 10 cm 6 cm
( i ) ( ii ) ( iii )
( i ) ( ii ) ( iii )
r t x
( i ) ( ii ) ( iii )
13' my; olajd we;s iup;=ri%j, § we;s ñkqï wkqj mßñ;sh fidhkak'
mßñ;sh - ''''''''''''''''''' mßñ;sh - '''''''''''''''''''''' mßñ;sh - '''''''''''''''''''''''
14'
mßñ;sh - ''''''''''''''' mßñ;sh - ''''''''''''''' mßñ;sh - '''''''''''''''
15'
16'
17' my; olajd we;s RcqfldaKdi%j, § we;s ñkqï wkqj mßñ;sh fidhkak '
4 cm 5 cm
2 cm
2 cm
2 cm2 cm
4 cm
4 cm 4 cm
5 cm
5 cm5 cm
a b
a
a
a
b b
b
m
m
m
m
2 cm2 cm 4 cm 4 cm
5 cm
5 cm
6 cm
6 cm
3 cm 3 cm
7 cm
7 cm

( i ) ( ii ) ( iii )
( i ) ( ii ) ( iii )
( i ) ( ii ) ( iii )
= 24 cm = 50 cm = 36 cm
= 8 cm = 15 cm = 10 cm
= .......... = .......... = .......
( i ) ( ii ) ( iii )
= 20 cm = 30 cm = 40 cm
= 4 cm = 5 cm = 5 cm
= .......... = .......... = .......
18'
5 cm
2 cm
3cm
8 cm 10 cm
5 cm
19'
mßñ;sh - ''''''''''''''''''' mßñ;sh - '''''''''''''''''''' mßñ;sh - '''''''''''''''''''
20'my; RcqfldaKdi%j, mßñ;sh yd È. § we;' tajdfha m<, fidhkak'
mßñ;sh mßñ;sh mßñ;sh
È. È. È.
m<, m<, m<,
21' my; RcqfldaKdi%j, mßñ;sh yd m<, § we;' tajdfha È. fidhkak'
mßñ;sh mßñ;sh mßñ;sh
m<, m<, m<,
È. È. È.
a
b
a
ab
m
n
m
n
b

22'§ we;s rEm w;=ßka ixhqla; ;, rEm f;dard " tu rEmj,g háka brla w¢kak'
23'
24'§ we;s rEm lÜg, w;=ßka ixhqla; ;, rEm lÜg,h f;dard háka brla w¢kak'
25' ksjerÈ ms<s;=r f;dard háka brla w¢kak'
ixhqla; ;, rEmhlg wjYH jkafka "
yev;, tlla muKs' $ yev;, lSmhls '
ixhqla; ;, rEmhlg yev;, "
tllaj;a wjYH fkdfõ' $ tllg jvd ;sìh hq;= hs'
ixhqla; ;, rEmhla kï tys yev;,"
tlsfklg iïnkaO úh hq;= h' $ fjka fjka j ;sìh hq;= h'
26' my; olajd we;s ixhqla; ;, rEm j, § we;s ñkqï wkqj mßñ;sh fidhd ;s;a br
u; ,shkak' ish¿ ñkqï olajd we;af;a fikaáógr j,sks'
'''''''''''''''''''''''''' ''''''''''''''''''''''' ''''''''''''''''''''''
( i )
(ii )
(iii)
( i )
(ii )
(iii)
( i ) (ii ) (iii)
3
2
5 5
5
5
5
5
3
3 3
2 2
4
10
6
6
2

27'
''''''''''''''''''''''' ''''''''''''''''''''''' '''''''''''''''''''''''
28'
'''''''''''''''''''''' '''''''''''''''''''''' '''''''''''''''''''''''''
29' § we;s W;a;rh w;ßka rEmfha mßñ;sh ±lafjk W;a;rh háka brla w¢kak'
30' my; m%ldYk yß o $ jerÈ o hkak f;dard ksjerÈ W;a;rh háka brla w¢kak '
jD;a;dldr fmdl=Kl jfÜ È. hkq tys mßñ;sh hs ' jD;a;fha mßñ;sh
tys mßêh kñka y÷kajhs' ^ yß $ jerÈ &
jD;a;dldr ldishl jfÜ È. tys mßêh fkdfõ' ^ yß $ jerÈ &
jD;a;hl mßêh hkq jD;a;fha mßñ;sh hs' ^ yß $ jerÈ &
31' jD;a;fha wrh l=ula ± hs fidhd wod< wlaIrh ;s;a br u; ,shkak'
''''''''''''' ''''''''''' '''''''''''''
( i ) (ii ) (iii)
( i ) (ii ) (iii)
a) 12 cm a) 26cm a) 8cm
b) 24cm b) 36cm b) 12cm
c) 8cm c) 22cm c) 22cm
( i )
(ii )
(iii)
( i ) (ii ) (iii)
d
a
b
r
m
n
3
8 4
4
5
2
6 cm
2 cm
2 cm
6 cm
2 cm
4 cm4 cm
6 cm
2 cm
10 cm
....
a
c
b
d
3a
a a
a a
b b
a
p
q
p
r
r
a
2

32' ksjerÈ W;a;rh f;dard háka brla w¢kak'
jD;a;hl wrh o " úIalïNh o kï " wrh yd úIalïNh w;r
iïnkaOh jkafka "
jD;a;hl mßêh fidhk iïnkaOh jkafka "
 j,ska ±lafjkafka
jD;a;hl wrh yd mßêh w;r iïnkaOhhs'
jD;a;hl úIalïNh yd mßêh w;r iïnkaOhhs'
33' ys w.h fidhd.kafka "
mrsêh u`.sks' mßêh u`.sks'
wrh úIalïNh
 ys wdikak w.h jkqfha "
34' § we;s o;a; wkqj my; jD;a;j, mßêh fidhkak' ^ flakaøh fõ' &
mßêh mßêh mßêh
35'
mßêh mßêh mßêh
rc 2
7 cm
14 cm
21cm
O O
O
7 cm
14 cm
28cm
O
OO
ys wdikak w.h oYu ia:dk 2 l g ,shQúg "
O
( i ) r d
a ) d = 2 r b ) r = 2 d
(ii )
a ) b ) 2
rA 
(iii)
a )
b )
( i ) 
a ) b )
(ii )
a )
7
22
b )
22
7
(iii) 
a ) 3.14 b ) 4.31
( i ) (ii ) (iii)
= ........ = ......... = .......
( i ) (ii ) (iii)
= ................. = ...................... = .......

mßñ;sh - 11
wkdjrK mÍlaIKh
W;a;r yd Wmfoia
m%Yak W;a;r Wmfoia
wxlh
1. (i) (ii) (iii)
2. (i) (ii)
(iii)
3. (i) 15cm (ii) 12cm (iii) 17cm
4. (i) 12cm (ii) 15cm (iii) 30cm
5. (i) 13cm (ii) 13cm (iii) 26cm
6. (i) 3a (ii) 3p (iii) 3m
7. (i) a+b+c (ii) p+q+r (iii) m+n+q
8. (i) 3a (ii) 3p (iii) 3r
9. (i) 2b+a (ii) 2p+r (iii) 2c+m
10. (i) 6cm (ii) 4cm (iii) 10cm
11. (i) 8cm (ii) 4cm (iii) 12cm
12. (i) 15cm (ii) 15cm (iii) 11cm
13. (i) 8cm (ii) 16cm (iii) 20cm
14. (i) 16cm (ii) 40cm (iii) 24cm
15. (i) 4a (ii) 4b (iii) 4m
16. (i) 4r (ii) 4t (iii) 4x
17. (i) 16cm (ii) 20cm (iii) 18cm
18. (i) 14cm (ii) 22cm (iii) 30cm
19. (i) 2a+2b (ii) 2m+2n (iii) 2a+2b
20. (i) 4cm (ii) 10cm (iii) 8cm
21. (i) 6cm (ii) 10cm (iii) 15cm
22.
23.
24.
25. (i)
(ii)
(iii)
26. (i) 22cm (ii) 28cm (iii) 26cm
27. (i) 16cm (ii) 22cm (iii) 16cm
28. (i) 2a+b+c (ii) 8a+2b (iii) 2p+q+2r
29. (i) b (ii) b (iii) c
30. (i) (ii) (iii)
31. (i) a (ii) b (iii) m
32. (i) a (ii) a (iii) b
33. (i) b (ii) a (iii) a
34. (i) 44cm (ii) 88cm (iii) 132cm
35. (i) 88cm (ii) 44cm (iii) 22cm
  
mßñ;sh fõ' jfÜ È.hs'
mßñ;sh fõ'
yev;, lSmhls '
tllg jvd ;sìh hq;= hs'
tlsfklg iïnkaO úh hq;= h'
yrs' jeros' yrs'
tall ,shd ;sìh hq;= hs}
tall ,shd ;sìh hq;= hs}
a + a + b wdldrhg iEfya'

j¾.M,h - I
ld¾h úYaf,aIKh
2'1 cHdñ;sl yev;, y÷kd .ekSu
2'2 ir, cHdñ;sl rEmj, j¾.M,h

j¾.M,h - I
wkdjrK mÍlaIKh
m%Yak wruqKq wruqKq
wxl wxl
2'1 cHdñ;sl yev;, y÷kd .ekSu'
1' 2'1'1 wm wjg we;s øjHj, kï l< yev we| olajhs '
2' 2'1'2 È we;s ;, rEm w;=ßka ixjD; ;, rEm f;darhs '
3' 2'1'3 § we;s ;, rEm w;=ßka ir, f¾Çh ixjD; ;, rEm f;darhs'
4' 2'1'4 § we;s ;, rEm w;=ßka jl% f¾Çh ixjD; ;, rEm f;darhs'
5' 2'1'5 § we;s ;, rEm w;=ßka ;%sfldaKdldr rEm f;darhs'
6' 2'1'6 § we;s ;, rEm w;=ßka YS¾I fldaK wkqj ;%sfldaKdldr rEm f;darhs'
7' 2'1'7 § we;s ;, rEm lSmhla w;=ßka ;%sfldaK fjkafldg olajhs'
8' 2'1'8 § we;s ;, rEm w;=ßka p;=ri% f;darhs'
9 2'1'9 Ys¾I fldaK wkqj p;=ri% f;darhs'
10 2'1'10 ir, f¾Çh ;, rEm lSmhla w;=ßka p;=ri% f;darhs '
11' 2'1'11 § we;s ;%sfldaK lSmhla w;=ßka iumdo ;%sfldaK f;darhs'
12' 2'1'12 § we;s ;%sfldaK lSmhla w;=ßka iuoaùmdo ;%sfldaK f;darhs'
13' 2'1'13 § we;s ;%sfldaK lSmhla w;=ßka úIu ;%sfldaK f;darhs'
14' 2'1'14 § we;s ;%sfldaK lSmhla w;=ßka RcqfldaKS ;%sfldaK f;darhs'
15' 2'1'15 § we;s p;=ri% lSmhla w;=ßka YS¾I fldaK RcqfldaK jk p;=ri%
f;darhs'
16' 2'1'16 § we;s p;=ri% lSmhla w;=ßka iup;=ri%% f;darhs'
17' 2'1'17 § we;s p;=ri% lSmhla w;=ßka RcqfldaKdi%% f;darhs'
18' 2'1'18 § we;s p;=ri% lSmhla w;=ßka frdïni f;darhs'
19' 2'1'19 § we;s p;=ri% lSmhla w;=ßka iudka;rdi% f;darhs'
20' 2'1'20 § we;s f;dr;=re wkqj p;=ri% lSmhla w;=ßka ;%mSishï f;darhs'
21' 2'1'21 § we;s rEm w;=ßka mßñ;shla iys; rEm f;darhs'
22' 2'1'22 § we;s rEm w;=ßka j¾.M,hla iys; rEm f;darhs'
23' 2'1'23 § we;s rEm w;=ßka ixjD; ;, rEm f;darhs'
24' 2'1'24 m%ldY lSmhla w;=ßka ;, rEmhl mßñ;sh fyda j¾.M,h ms<sn|
±lafjk m%ldYh f;darhs'
25' 2'1'25 wjg mßirfha yev;, 2 la w;=ßka j¾.M,fhka úYd, yev;,h
f;darhs'
2'2 ir, cHdñ;sl rEmj, j¾.M,h'
26' 2'2'1 iup;=ri%dldr fldgq iys; rEmhl mrsñ;sh fldgq weiqrska ,shd olajhs'
27' 2'2'2 iup;=ri%dldr fldgq iys; rEmhl j¾.M,h " fldgqjl j¾.M,h
tall tlla f,i i,ld m%ldY lrhs'
28' 2'2'3 iup;=ri%dldr fldgq iys; rEmhl j¾.M,h wNsu; tall j,ska
j.=jl olajhs'
29' 2'2'4 fldgq cd,hla u; we| we;s ;%sfldaKhl j¾.M,h o< jYfhka wNsu;
tallj,ska olajhs'
30' 2'2'5 mdoj, ñkqï ,l=Kq l< rEmj, j¾.M,h ±laùug Ndú;jk tall
,shd olajhs'

j¾.M,h I
wkdjrK mÍlaIKh
m%Yak m;%h
1' wjg mßirfha olakg ,efnk øjH we;=<;a my; j.=j iïmQ¾K lrkak'
yevh w¢kak
.=refïi ,E,af,a u;=msg
l¿ ,E,a, u;=msg
f.ìu
odÿleghl uqyqK;
fíifï m;=,
lsß áka tll uqyqK;
úys; p;=ri%h
2' my; ±lafjk rEm w;=ßka ixjD; ;, rEm f;dard tu rEmj,g háka brla
w¢kak'
3' my; ±lafjk rEm w;=ßka ixjD; rEm f;dard tu rEmj,g háka brla w¢kak'
4' my; ±lafjk rEm w;=ßka jl% f¾Çh rEm f;dard tu rEmj,g háka brla
w¢kak'
( i )
(ii)
(iii)
( iv )
( v )
( vi )
(vii)

5' my; ±lafjk rEm w;=ßka ir, f¾Ld LKav ;=klska muKla iEÿKq rEm f;dard
tu rEmj,g háka brla w¢kak'
6' YS¾I fldaK ;=kla iys; ir, f¾Çh ixjD; rEm" my; rEm w;ßka f;dard tu
tla tla rEmhg háka brla w¢kak'
7' my; ±lafjk rEm w;=ßka ;%sfldaK f;dard tajd háka brla w¢kak'
8' my; ±lafjk rEm w;=ßka ir, f¾Ld LKav y;rlska muKla iEÿKq ixjD;
;, rEm f;dard tu tla tla rEmhg háka brla w¢kak'
9' my; ±lafjk rEm w;=ßka YS¾I fldaK y;rla muKla we;s ixjD; ;, rEm
f;dard" tu tla tla rEmhg háka brla w¢kak'
10' my; ±lafjk rEm w;=ßka p;=ri% f;dard" tu tla tla rEmhg háka brla
w¢kak'

3cm
4cm
6cm
5cm
4cm
3cm
11' my; ±lafjk rEm w;=ßka iumdo ;%sfldaK f;dard" tu tla tla rEmhg háka
brla w¢kak'
4 cm 5 cm
4 cm
5 cm
5 cm
12' my; ±lafjk ;%sfldaK w;ßka iu oaùmdo ;%sfldaK f;dard" tu tla tla
rEmhg háka brla w¢kak'
13' my; ±lafjk ;%sfldaK w;ßka " úIu ;%sfldaK f;dard tu tla tla rEmhg
háka brla w¢kak'
14' my; ±lafjk ;%sfldaK w;ßka " RcqfldaKsl ;%sfldaK f;dard tu tla tla
15' my; ±lafjk rEm w;=ßka YS¾I fldaK RcqfldaK jQ p;=ri% f;dard" tu tla tla
16' my; ±lafjk rEm w;ßka iup;=ri% f;dard" tu tla tla rEmhg háka brla
w¢kak'
5cm
5cm
5cm
5cm
5cm
2cm
4cm 4cm
3cm
4cm
5cm

17' my; ±lafjk rEm w;ßka RcqfldaKdi% f;dard" tu tla tla rEmhgháka brla
w¢kak'
4cm
2cm2cm
5cm
2cm
18' my; ±lafjk rEm w;ßka frdïni f;dard" tu tla tla rEmhg háka brla
w¢kak'
5cm 4cm
2cm
2cm
2cm
2cm
19' my; ±lafjk rEm w;ßka iudka;rdi% f;dard" tu tla tla rEmhg háka brla
w¢kak'
20' my; ±lafjk rEm w;ßka ;%mSishï f;dard" tu tla tla rEmhg háka brla
w¢kak'
21' my; ±lafjk rEm w;ßka jfÜ È.la .;yels rEm f;dard" tu tla tla rEmhg
háka brla w¢kak'
22' my; ±lafjk rEm w;ßka jgjk bv m%udKhla wvx.= rEm f;dard" tu tla tla
5cm
5cm
2cm
2cm

( i )
(ii )
(iii)
23' my; ±lafjk rEm w;ßka jfÜ È.la yd jgjQ bv m%udKhla iys; rEm f;dard"
tu tla tla rEmhg háka brla w¢kak'
24' my; yd ys " m%ldYhg .e<fmk wjia:dj hk wjia:d
w;=ßka f;dard ksjerÈ W;a;rhg háka brla w¢kak'
;, rEmhl jgjk bv m%udKh m%ldY jkafka "
mßñ;sfhka '
j¾.M,fhka '
YS¾I fldaK j,ska '
;, rEmhl jfÜ È. m%ldY jkafka "
mßñ;sfhka '
j¾.M,fhka '
YS¾I fldaKj,ska '
25' my; ±lafjk tla tla yev;,j, j¾.M, hq., ne.ska jvd úYd, j¾.M,h
wh;a yev;,h j.=fõ wod< fma<sfha ysia;ek u; ,shkak'
j¾.M,h ±lafjk yev;, hq.,h' jvd úYd, j¾.M,hwh;a yev;,h
yd mka;s ldur f.ìu ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
odÿleghl uqyqK; yd
.=refïi ,E,af,a u;=msg ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
.Ks; fm<fmdf;a msgqj
yd m;a;r msgqj '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
26' my; ±lafjk rEmj, l=vd fldgqjl me;a;l È. tall tlla f,i f.k tla
tla rEmfha mßñ;sh ysia ;ek u; ,shkak'
'''''''''''''''''''''''''' ''''''''''''''''''''' '''''''''''''''''''''''''
a. b. ( i ) ( ii )(iii )
a.
( i )
(ii )
(iii)
b.
( i )
(ii )
(iii)

27' my; ±lafjk rEmj, l=vd fldgqjl j¾.M,h j¾. tall 1 f,i i,lñka "
tu rEmj, j¾.M, fidhd rEmhg háka ysia;ek u; ,shkak'
'''''''''''''''''''''''''' ''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''
2 8'
by; rEm weiqfrka my; j.=j iïmQ¾K lrkak' mßñ;h i|yd fldgqjl È.
tall 1 la f,i;a " j¾.M,h i|yd l=vd fldgqjl j¾.M,h j¾. tall 1 la
f,i;a i,lkak'
rEmh mßñ;sh j¾.M,h
''''''''''''''''''''' '''''''''''''''''''''''
''''''''''''''''''''' '''''''''''''''''''''''
''''''''''''''''''''' '''''''''''''''''''''''
29' my; oelafjk fldgq cd,lh ;=< we;<;a lr we;s ;%sfldaKdldr rEmj,ska
jgjk j¾.M,h " fldgq .Kka lr ysia ;eka u; ,shkak' fldgqjlska fldgia
.Kka lsÍfï § nd.hlg jvd jeä kï tlla f,i;a " fldgqjla j¾. tallhla
f,i;a i,lkak'
a b c
a
b
c
a.
b.
c.
a. ..................
b. ..................
c. ..................

( i ) (ii ) (iii)
( iv ) ( v ) ( vi )
30' my; ±lafjk ñkqï iys; rEmj, j¾.M,h ,nd .ekSfï § tu j¾.M, ,shd
olajk tallh tu tla tla rEmhg háka ,shkak '
''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''
''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''
5cm 5cm
2cm
4 cm
10cm
4m
2m
tall 3
tall 3
tall 4

j¾.M,h I
wkdjrK mÍlaIKh
W;a;r yd Wmfoia
m%Yak
wxlh W;a;r Wmfoia
1' yevh y÷kdf.k tu yevh
o< rEmhlska wÈhs'
2'
3'
4'
5'
6'
7'
8'
9'
i. v.
ii vi.
iii' vii.
iv
m%Yak wxl 2 - 10 f;la oS
we;s rEmj,ska " wod<
rEmj,g háka brla we|
;sìh hq;= h'
jegySulska f;drj rEm
,l=Kq lr ;sfnk nj
fmfka kï ie,ls<su;a úh
hq;= h'
tjeks YsIHhka iïuqL
idlÉPdjlg fhduqlr
.ksñka ixjD; yd újD; nj
ms<sn| j m%Yak úuikak'

m%Yak
wxlh W;a;r Wmfoia
10'
11'
12'
13'
14'
15'
16'
5cm
5cm 5cm
5cm
17' 2cm2cm2cm
5cm
4cm
4cm
18'
4cm
2cm
2cm
2cm
2cm
19'
5cm
5cm
2cm
2cm
20'
21'
22'
23'
rEmj, mdo yd fldaK u; i,l=Kq
lr we;s ixfla; yÿkd .ekSu yd tu
ixfla; wkqj rEmh kï lsßfï
yelshdj'
j¾.M,h we;=<;a .eg¨j, § mdo u;
i,l=Kq lrk ,o ixfla; u.ska rEm
y÷kd.; yels ùu wfmalaIs;hs'
jfÜ È.la ,nd .ekSug ixjD;
rEmhla ;sîu w;HjYH fõ'
rEmfhka jgjk bv m%udKh i|yd
ixjD; rEmhla u úh hq;= h'
jfÜ È.;a " jgjk j¾.M,h;a hk
fol u tl u ;, rEmhl tljr
;sfnk nj ms<sn| wjOdkh fhduq
lrkak'
4 cm
4 cm
5 cm 5 cm
5 cm
3cm 4cm
5cm
5cm
4cm
3cm
5cm
4cm
3cm

24' j¾.M,fhka
mßñ;sfhka
25' mka;s ldur f.ìu
m;a;r msgqj
26' tall 14
tall 12
tall 16
27' j¾. tall 12
j¾. tall 9
j¾. tall 7
28' rEmh mßñ;sh j¾.M,h
tall 16 j¾. tall 16
tall 16 j¾. tall 15
tall 16 j¾. tall 7
29' j¾. tall 6
j¾. tall 5
j¾. tall 9
30' j¾. fikaáóg¾ fyda
j¾. fikaáóg¾ fyda
j¾. fikaáóg¾ fyda
j¾. óg¾ fyda
j¾. tall
j¾. tall
a.
b.
( i )
(ii )
(iii)
( i )
(ii )
(iii)
( i )
(ii )
(iii)
a
b
c
( a )
( b )
( c )
( i ) cm2
(ii ) cm2
(iii) cm2
( iv ) m2
( v )
( vi )
rEmhlska jgjk bv m%udKh
tys j¾.M,h f,i;a " jfÜ
È. mßñ;sh f,i;a ksrjq,a j
wjfndaO ù ;sìh hq;= h' tfia
fkdue;s nj fmfka kï
iïuqL idlÉPdjlg fhduq
lsÍu wjYH fõ'
j¾.M,h iei£ug mßirfha
we;s ;, rEmj, m%udKh
ms<sn| jegySu wfmalaIs; hs'
fldgqjl È. tallh f,i
ie,fla'
y;/ia fldgqjl j¾.M,h
j¾. tallhla f,i ie,fla'
mßñ;sh iudk jqj;a j¾.M,h
fjkia úh yels nj'
ms<s;=r wdikak fldgq .Kk
f,i ;sîu iEfya'
È. ñkqï wkqj j¾.M,h iu.
tallh ielfik nj'

j¾.M,h - II
ld¾h úYaf,aIKh
2'3 RcqfldaKdi%j, j¾.M,h
2'4 ;%sfldaKj, j¾.M,h
2'5 iudka;rdi%j, j¾.M,h
2'6 ;%mSishul j¾.M,h

j¾.M,h II
wkdjrK mÍlaIKh -
iúia;r ld¾h úYaf,aIKh
m%Yak wruqKq wruqKq
wxlh wxlh
2'3 RcqfldaKdi%hl j¾.M,h'
1' 2'3'1 RcqfldaKdi%hl È. yd m<, ñkqï § we;s úg tu ñkqï weiqßka tys
j¾.M,h ms<sn| m%ldYhla ,shhs'
2 2'3'2 RcqfldaKdi%hl os. yd m<, oS we;s úg tys j¾.M,h fidhhs'
3 2'3'3 RcqfldaKdi%hl j¾.M,h yd m<, § we;s úg RcqfldaKdi%fha È.
i|yd m%ldYkhla ,shhs'
4' 2'3'4 RcqfldaKdi%hl j¾.M,h yd m<, § we;s úg È. .Kkh lrhs'
5' 2'3'5 mdoj, ñkqï § we;s úg iup;=ri%hl j¾.M,h fiùu i|yd
m%ldYkhla" § we;s ñkqï weiqßka ,shhs'
6' 2'3'6 mdoj, ñkqï § we;s iup;=ri%hl j¾.M,h fidhhs'
7' 2'3'7 j¾.M,h § we;s iup;=ri%hl me;a;l È. fiùu i|yd m%ldYkhla" §
' we;s ñkqï weiqßka ,shhs'
8' 2'3'8 j¾.M,h § we;s iup;=ri%hl me;a;l È. fidhhs'
2'4 ;%sfldaKhl j¾.M,h'
9' 2'4'1 mdoj, ñkqï § we;s RcqfldaKS ;%sfldaKhl j¾.M,h ±laùu i|yd
m%ldYkhla ,sùug wjYH ñkqï muKla ,shd olajhs'
10' 2'4'2 RcqfldaKS ;%sfldaKhl mdoj, ñkqï § we;s úg" § we;s ñkqï weiqßka
;%sfldaKfha j¾.M,h i|yd m%ldYkhla ,shd olajhs'
11' 2'4'3 RcqfldaKS ;%sfldaKhl mdoj, ñkqï § we;s úg" tlsfkl ,ïn mdo
y÷kd .ksñka ;%sfldaKfha j¾.M,h .Kkh lrhs'
12' 2'4'4 RcqfldaKS ;%sfldaKhl j¾.M,h yd RcqfldaKh wvx.= mdo foflka
tll È. § we;s úg tys j¾.M,h iólrKhlska ,shd olajhs'
13' 2'4'5 RcqfldaKS ;%sfldaKhl j¾.M,h yd RcqfldaKh wvx.= mdo foflka
tll È. § we;s úg tys wfkla mdofha È. .Kkh lrhs'
14' 2'4'6 YS¾Ihl isg mdohlg ,ïnhla we| we;s ;%sfldaK lSmhl wdOdrl
mdoh yd ,ïN Wi y÷kd f.k j.= .; lrhs'
15' 2'4'7 ;%sfldaKhl § we;s ñkqï w;ßka tys j¾.M,h fiùug wjYH ñkqï
f;dardf.k ,shd olajhs'
16' 2'4'8 ;%sfldaKhl wdOdrlh yd ,ïn Wfiys ñkqï § we;s úg tu ñkqï
weiqßka j¾.M,h fiùu i|yd m%ldYkhla ,shhs'
17' 2'4'9 ;%sfldaKhl wdOdrlh yd ,ïn Wfiys ñkqï § we;s úg tys j¾.M,h
.Kkh lrhs'
18' 2'4'10 ;%sfldaKhl j¾.M,h yd wdOdrlfha Èf. ys ñkqï § we;s úg iy
,ïn Wi ùÔh ixfla;hlska olajd we;s úg tu rdYSka w;r
iïnkaOh iólrKhlska olajhs'
19' 2'4'11 ;%sfldaKhl j¾.M,h yd wdOdrlfha ñkqï § we;s úg ;%sfldaKfha
,ïn Wi .Kkh lrhs'

20' 2'4'12 ;%sfldaKhl j¾.M,h yd ,ïn Wfiys ñkqï § we;s úg wdOdrlfha
È.,nd .ekSug wjYH m%ldYkh ,shd olajhs '
2'5 iudka;rdi%j, j¾.M,
21' 2'5'1 iudka;rdi%hl mdoj, ñkqï yd mdo w;r ,ïn ÿr § we;s úg tu ñkqï
w;ßka ,ïn ÿr ±lafjk ñkqu y÷kd f.k ,shd olajhs'
22' 2'5'2 mdoj, È. yd ,ïn ÿr ,l=Kq l< rEm w;=ßka" j¾.M,h fiùug wjYH
ñkqï iys; rEm y÷kd f.k ,shd olajhs'
23' 2'5'3 iudka;rdi%hl mdoj, È. yd mdo folla w;r ,ïn ÿr § we;s úg tu
ñkqï weiqßka j¾.M,h fiùug m%ldYkhla ,shd olajhs'
24' 2'5'4 frdïnihl mdohl È. yd mdo folla w;r ,ïn ÿr § we;s úg
frdïnifha j¾.M,h .Kkh lrhs'
25' 2'5'5 frdïnihl j¾.M,h yd mdohl ñkqï § we;s úg mdo folla w;r ,ïn
ÿr i|yd m%ldYkhla § we;s ñkqï weiqßka ,shhs'
26' 2'5'6 frdïnihl j¾.M,h yd wdOdrlfha ñkqï § we;s úg mdo w;r ,ïn
ÿr .Kkh lrhs'
27' 2'5'7 iudka;rdi%hl noaO mdo foll iy mdo folla w;r ,ïn ÿr § we;s úg
tu ñkqï weiqßka tys j¾.M,h fiùu i|yd m%ldYkhla ,shhs'
28' 2'5'8 iudka;rdi%hl noaO mdo foll iy mdo folla w;r ,ïn ÿr § we;s úg
tys j¾.M,h .Kkh lrhs'
29' 2'5'9 iudka;rdi%hl mdohla fyda mdo folla w;r ,ïn ÿr iuÕ j¾.M,h §
we;s úg mdo folla w;r ,ïn ÿr fyda mdohl È. iïnkaO m%ldYkhla
§ we;s ñkqï weiqßka ,shd olajhs'
2'6 ;%smSishul j¾.M,h'
30' 2'6'1 ;%mSishul iudka;r mdo foflys iy tu mdo fol w;r ,ïn ÿfrys
ñkqï § we;s úg tu ñkqï weiqßka ;%mSishfï j¾.M,h ±laùu i|yd
m%ldYkhla ,shd olajhs'
31' 2'6'2 ;%mSishul iudka;r mdo foflys iy tu mdo fol w;r ,ïn ÿfrys
ñkqï § we;s úg tys j¾.M,h .Kkh lrhs'
32' 2'6'3 ;%mSishul j¾.M,h iy iudka;r mdo foflys ñkqï § we;s úg iy
iudka;r mdo fol w;r ,ïn ÿr ùÔh ixfla;hla u`.ska olajd we;s úg
tu rdYSka w;r iïnkaOh iólrKhla u`.ska olajhs'
33' 2'6'4 ;%mSishul j¾.M,h iuÕ iudka;r mdo foflka tll È. iy
iudka;r mdo fol w;r ,ïn ÿr § we;súg b;sß iudka;r mdofha È.
fiùug iqÿiq iólrKhla f.dvkÕhs'
34' 2'6'5 ;%mSishul j¾.M,h " iudka;r mdo fol w;r ,ïn ÿr iy tla
iudka;r mdohl ñkqï § we;s úg wfkla iudka;r mdofha È. .Kkh
lrhs'

wkdjrK mÍlaIKh
j¾.M,h - ii
m%Yak m;%h
1' my; ±lafjk tla tla RcqfldaKdi%fha j¾M,h ,nd .ekSug wod< m%ldYkhla
§ we;s ñkqï wkqj ,shkak' ^ iq¿ lsÍu wjYH ke;' &
a m
10cm
5cm
4cm
6cm
b m
'''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''
2' my; ±lafjk tla tla RcqfldaKdi%fha j¾.M,h fidhkak'
6cm
10cm
5cm 4cm
5 m
2 m
''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''
3' j¾.M,h yd m<, § we;s my; ±lafjk RcqfldaKdi%fha È. fiùu i|yd § we;s
ñkqï wkqj m%ldYkhla ,shkak' ^ W;a;rh iq¿ lr ±laùu wjYH ke;' &
72m2
35 cm2
40 cm2
4cm
5cm
8 m
''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''
4' j¾.M,h yd m<, § we;s my; ±lafjk RcqfldaKdi%fha È. fidhkak'
72m2
35 m2
40cm2
4cm
5 m
8 m
'''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''
i. ii. iii.
i. ii. iii.
i. ii. iii.
i. ii. iii.

5' my; ±lafjk tla tla iup;=ri%fha j¾.M,h fiùu i|yd § we;s ñkqï wkqj
m%ldYkhla ,shkak' ^ W;a;rh iq¿ lr ±laùu wjYH ke;' &
5cm
5cm
5cm
5cm
6cm
6cm
6cm6cm
x cm
'''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''
6' my; olajd we;s ñkqï wkqj tla tla iup;=ri%fha j¾.M,h fidhkak'
6cm
6cm
6cm6cm
3 cm
5 m
3 cm 3 cm
3 cm
5 m
5 m
5 m
''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''
7' j¾.M,h § we;s my; ±lafjk tla tla iup;=ri%fha me;a;l È. fiùu i|yd
m%ldYkhla ,shkak' ^ W;a;rh iq¿ lr ±laùu wjYH ke;' &
100 cm
2
49 m
2
1 cm2
''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''
8' j¾.M,h § we;s my; ±lafjk tla tla iup;=ri%fha me;a;l È. fidhkak'
100 m
2
49 cm2
1 m2
''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''
i . ii . iii.
i. ii. iii.
i. ii. iii.
i. ii. iii.

9' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h ,nd .ekSu i|yd" tu
;%sfldaKj, i|yka lr we;s ñkqïj,ska wjYH jk ñkqï muKla f;dard ;s;a
fm< u; ,shkak'
4 cm
3 cm 5 cm 8 m
6 m
10 m
a m
b m
c m
''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''
10' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h ,nd .ekSu i|yd" §
we;s ñkqï we;=<;a m%ldYkhla ;s;afm< u; ,shkak' ^ iq¿ lsÍu wjYH ke;'&
10 cm4 cm
3 cm 5 cm 8 cm
6 cm
10 cm
8 cm
x cm
''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''
11' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h fidhkak'
4 cm
3 cm 5 cm 8 m
6 m
10 m
8 m
10
cm
x m
'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''
12' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h yd RcqfldaKh wvx.=
tla mdohl ñkqï § we;' RcqfldaKh wvx.= wfkla mdoh jk ,nd .ekSu
i|yd § we;s f;dr;=re we;=<;a iólrKhla ,shkak'
5 cm
x 10 m 8 m
10 cm2
20 m2
16m2x
x
'''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''
13' my; ±lafjk tla tla RcqfldaKS ;%sfldaKfha j¾.M,h yd Rcq fldaKh wvx.=
tla mdohl ñkqï § we;' RcqfldaKh wvx.= wfkla mdofha È. fidhkak'
5 m
10 cm 810 m
2
20 cm2
48 cm2
''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
x
i. ii. iii.
i. ii. iii.
i. ii. iii.
i. ii. iii.
i. ii. iii.

14' my; ±lafjk tla tla ;%sfldaKfha we;=<;a lr we;s f;dr;=re weiqßka" § we;s
j.=j iïmQ¾K lrkak'
A
B D C K N M
R
L
P
;%sfldaKh wdOdrl mdoh ,ïn Wi
1. ABC ..................... .......................................
2. PQR ..................... .......................................
3. KLM ..................... .......................................
15' my; oelafjk ;%sfldaKhkays mdoj, oS we;s ñkqïj,ska tu tla tla
;%sfldaKfha j¾.M,h ,nd .ekSu i|yd wjYH jk ñkqï my; ;s;a fm< u;
,shkak'
6cm 4cm 6 cm
10 cm
12 m
12m x m 12m 8 cm
6 cm
4 cm
3 cm
'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''
16' my; oelafjk tla tla ;%sfldaKhkays j¾.M,h ,nd .ekSu i|yd oS we;s ñkqï
iïnkaO lr m%ldYk ,shkak' ^ iq¿ lsÍu wjYH fkdfõ' &
10 cm
5 cm
12 cm
8 m
5 m
4 cm
5 cm
'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''
Q
S
i. ii. iii.
i. ii. iii.
i. ii. iii.

17' my; oelafjk tla tla ;%sfldaKfha j¾.M,h .Kkh lrkak'
10 m
5 cm
12 cm
8 cm
5 cm
4 m
5 cm
''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''
18' my; ±lafjk tla tla ;%sfldaKfha j¾.M,h yd wdOdrl mdofha ñkqï § we;'
j,ska ±lafjk ,ïn Wi fiùu i|yd § we;s ñkqï we;=<;a iólrKhla
,shkak'
10 cm
12 m
h
h
h
8 cm
''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''
19' j¾.M,h yd wdOdrl mdoj, ñkqï § we;s my; ±lafjk tla tla ;%sfldaKfha
j,ska ±lafjk ,ïn Wi fidhkak'
10 cm
12 m
h
h
h
8 cm
'''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''
20' j¾.M,h yd ,ïn Wi § we;s my; ±lafjk tla tla ;%sfldaKfha f,i
±lafjk wdOdrl mdofha È. ,nd .ekSu i|yd § we;s ñkqï we;=<;a m%ldYkhla
,shkak' ^ iq¿ lsÍu wjYH fkdfõ' &
x
x
6 cm
5 m
4 cm
x< >
< >
'''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''
x
= 16 cm2
= 20 cm2
= 36 m2
j¾.M,h j¾.M,h j¾.M,h
j¾.M,h j¾.M,h j¾.M,h= 16 cm2
= 50 cm2
= 36 m2
h
h
j¾.M,h j¾.M,h j¾.M,h= 20 cm2
= 24 cm2
= 36 m2
i. ii. iii.
i. ii. iii.
i. ii. iii.
i. ii. iii.

21' my; iudka;rdi%j, olajd we;s ñkqïj,ska" iïuqL mdo w;r ,ïn ÿr ±lafjk
ñkqu f;dard" ;s;a br u; ,shkak'
12 cm 16 cm
15 cm
12 cm
15 cm
16 cm
12 cm8 cm Xx8 cm
15 cm
15 cm 8 cm
'''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''
22' my; ±lafjk p;=ri% w;ßka j¾.M,h fiùug m%udKj;a o;a; ,l=Kq l< rEm
igyka háka brla w¢kak'
23' my; ±lafjk iudka;rdi%j, olajd we;s ñkqï weiqßka tajdfha j¾.M, ±lafjk
m%ldYhla ;s;a bru; ,shkak' ^ iq¿ lsÍu wjYH fkdfõ' &
8 cm Xx8 cm
6 cm
6 cm
10 cm
8 cm12 cm
15 cm
12 cm5 cm 8 cm
12 cm
''''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''
24' my; ±lafjk tla tla frdïnifha j¾.M,h fidhkak'
6 cm
5 cm 12 cm12 cm
8 cm
6 cm
10 cm
8cm
''''''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''
8 cm Xx8 cm
4 cm
6 cm
4 cm
6 cm
5 cm
6 cm
4 cm
8 cm
6 cm6 cm
10 cm
5 cm 7 cm
i. ii. iii.
i. ii. iii.
i. ii. iii.
12cm

25' my; ±lafjk tla tla frdïnifha j¾.M,h yd wdOdrl mdofha È. § we;'
f,i ±lafjk ,ïn Wi ,nd .ekSu i|yd § we;s ñkqï we;=<;a m%ldYkhla
;s;a br u; ,shkak' ^ iq¿ lsÍu wjYH fkdfõ' &
12 cm12 cm
8 cm
h
10 m
h
9 cm
h
''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
26' my; ±lafjk tla tla frdïnifha j¾.M,h yd wdOdrl mdofha È. § we;' tla
tla frdïnifha ,ïn Wi fidhkak'
12 cm12 cm
8 cm
h
9 cm
h
10 m
h
''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
27' my; ±lafjk tla tla iudka;rdi%fha j¾.M,h ,nd .ekSu i|yd § we;s ñkqï
we;=<;a lrñka m%ldYkhla ne.ska ;s;a br u; ,shkak' ^iq¿ lsÍu wjYH fkdfõ' &
10 cm
5cm 12 cm12 cm
12 cm
5cm
8 cm
6 cm
6 m
5cm
12 cm12 cm
10 m 4 m
''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''
28' my; ±lafjk tla tla iudka;rdi%fha j¾.M,h fidhkak'
'''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''
'''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''''
h
= 40 m2
= 45 cm2
= 24 cm2
= 40 m2
= 45 cm2
= 24 cm2
10 cm
5cm 12 cm12 cm
12 cm
5cm
8 cm
6 cm
6 m
5cm
12 cm12 cm
10 m 4 m
i. ii. iii.
i. ii. iii.
i. ii. iii.
i. ii. iii.

29' my; iudka;rdi%j, j¾.M,h yd ;j;a tla ñkqula olajd we;' j¾.M,hg
iïnkaO wfkla ñkqu ,nd .ekSu i|yd" tu ñkqu yd j¾.M,h iïnkaO lrk
m%ldYkhla my; ;s;a fm< u; ,shkak'
12 cm12 cm
6 cm
2 m
10 cm
''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
30' my; oelafjk tla tla ;%mSishfïj¾.M,h ,nd .ekSu i|yd § we;s ñkqï
we;=<;a m%ldYkhla ;s;a br u; ,shkak' ^ W;a;rh iq¿ lsÍu wjYH fkdfõ' &
>
>
>
>
^
^
^
4 m
5 m
10 m
3 cm
5 cm
9 cm
x
2 m
y
''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''
''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''
''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''
31' my; ±lafjk tla tla ;%mSishfï j¾.M,h fidhkak'
>
>
>
>
^
^
^
4 m
5 m
10 m
3 cm
5 cm
9 cm
x
2 m
y
'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''
'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''
'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''
'''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''
= 30 cm2
= 24 cm2
= 12 m2
h
x
x
i. ii. iii.
i. ii. iii.
i. ii. iii.

32' fuys olajd we;s tla tla ;%mSishfï j¾.M,h yd iudka;r mdo j, ñkqï § we;'
iudka;r mdo fol w;r ,ïn ÿr jk ,nd .ekSu msKsi" § we;s f;dr;=re
we;=<;a iólrKhla ;s;a br u; ,shkak' ^ W;a;rh iq¿ lsÍu wjYH fkdfõ' &
>
>
^
^ >
>
2 m
h
8 m
7 m 5 m
h
4 cm
h
8 cm
'''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
'''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
33' fuys olajd we;s tla tla ;%mSishfï j¾.M,h " iudka;r mdo hq.,fhka tll
È. yd iudka;r mdo w;r ,ïn ÿr § we;' tu ñkqï wkqj j,ska olajd we;s
mdofha È. ,nd .ekSu i|yd iqÿiq iólrKhla ,shkak' ^ iólrKh úi£u
wjYH fkdfõ' &
>
>
^
^ >
>
x
4 m
10 m
x 4cm
5cm
4 m
6 m
x
''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
34' my; ±lafjk tla tla ;%mSishfï j,ska ±lafjk w.h fidhkak'
>
>
^
^ >
>
x
4 m
10 m
x 4cm
5cm
4 m
6 m
x
''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
''''''''''''''''''''''''''''''''''''''''''' '''''''''''''''''''''''''''''''''''''''''''''' ''''''''''''''''''''''''''''''''''''''''''''
h
x
x
= 40 m2
= 30 m2
= 18 cm2
= 24 m2
= 30 cm2
= 36 m2
= 24 m2
= 30 cm2
= 36 m2
i. ii. iii.
i. ii. iii.
i. ii. iii.

j¾.M,h - 11
wkdjrK mÍlaIKh
W;a;r yd Wmfoia
1. i. (510) cm2
ii. (64) cm2
iii.(ab)m2
2. i. 50 cm2
ii. 24 cm2
iii.10m2
3. i. 40/4 ii.35/5 iii.72/8
4. i. 10 cm ii.7m iii.9m
5. i. 66 ii. 55 iii.x2
6. i. 36 cm2
ii. 25 m2
iii.9cm2
7. i. 2
cm100 ii. 2
49m iii. 2
cm1
8. i.10m ii.7cm iii.1m
9. i.3cm,4cm ii.8m,6m iii.am,bm
10. i. 34
2
1
 ii. 86
2
1
 iii. 810
2
1

11. i. 6cm2
ii. 24 m2
iii.40m2
12. i. 105
2
1
 x ii. 2010
2
1
 x iii. 168
2
1
 x
13. i. 4 cm ii. 4cm iii.12cm
14. ;%sfldaKh wdOdrl mdoh ,ïn Wi
ABC BC AD
PQR PQ RS
KLM KM LN
15. i.10cm,4cm ii. 12m,x m iii.8cm,3cm
16. i. 410
2
1
 ii. 512
2
1
 iii. 58
2
1

17. i. 20 m2
ii. 30 cm2
iii.20 cm2
18. i. 168
2
1
 h ii. 2010
2
1
 h iii. 3612
2
1
 h
19. i. h = 4 cm ii. 10 cm iii.6m
20. i. 205
2
1
 x ii.
1
4 24
2
x  iii. 366
2
1
 x
21. i. 8 cm ii. 12 cm iii.12cm
22.
4 cm
6 cm
6 cm
4 cm
8 cm
6 cm6 cm
10 cm
5 cm 7 cm
m%Yak W;a;r Wmfoia
wxlh

23. i. 56 ii. 815 iii. 108
24. i. 30 cm2
ii.48cm2
iii.80cm2
25. i. 4010 h ii. 459 h iii. 248 h
26. i. 4 m ii. 5cm iii.3cm
27. i. 510 ii. 56  iii. 410
28. i. 50 cm2
ii. 30 cm2
iii.40m2
29. i. 310 h 0 ii. 246 x iii. 122 x
30. i. 5
2
104


ii. 5
2
93


iii. 2
2

 yx
31. 35 m2
ii. 30 cm2
iii.x+ym2
32. i. 40
2
)82(


h ii. 30
2
)57(


h
iii. 18
2
)84(


h
33. i. 244
2
)10(

x
ii. 305
2
)4(

 x
iii. 366
2
)4(

x
34. 2 m ii. 8cm iii.8cm

mßudj
ld¾h úYaf,aIKh
3'1 >k jia;= y÷kd.ekSu
3'2 >klhl yd >kldNhl mßudj
3'3 ;%sfldaK ms%siauhl mßudj

3' mrsudj
wkdjrK mÍlaIKh
m%Yak wruqKq Wmfoia
wxlh wxlh
3'1 >k jia;= y÷kd.ekSu'
1' 3'1'1 fok ,o ,ehsia;=jlska ;, rEm yd >kjia;= fjka lr olajhs'
2' 3'1'2 fok ,o øjH ish,a,gu wjldYfha bvla wjYH jk nj m%ldY lrhs'
3' 3'1'3 mßirfha olakg we;s úúO >k jia;+j, uQ,sl yevh y÷kajk ku
,shd olajhs'
4' 3'1'4 ñkqï olajd we;s >klhl" me;a;l È. fjka lr ,shd olajhs'
5' 3'1'5 ñkqï olajd we;s >klhl È." m<, yd Wi fjka fjka j ,shd olajhs'
3'2 >klhl yd >kldNhl mßudj
6' 3'2'1 leghla weiqßka " Wi jQ úúO m%udKfha >kldNj, mßudj
,shd olajhs'
7' 3'2'2 Wi jQ >kldNhl mßudj .Kkh lrhs'
8' 3'2'3 fikaáógr tallj,ska ñkqï § we;s >kldNhl mßudj .Kkh lrhs'
9' 3'2'4 ñkqï tall ógrj,ska § we;s >kldNhl mßudj .Kkh lrhs'
10' 3'2'5 >klhl mßudj .Kkh lrhs'
11' 3'2'6 fok ,o >k jia;=jl ;,hlg iudka;r j ,efnk yrialv tl u
m%udKfhka yd tl u yevfhka hqla; nj ksÍlaIKh lr m%ldY lrhs'
12' 3'2'7 fok ,o >kjia;=j, taldldr yrialvla mj;sk nj fyda fkdmj;sk
nj m%ldY lrhs'
13' 3'2'8 fok ,o >kldNhl " § we;s ñkqï wkqj yrialv j¾.M,h .Kkh
lrhs'
14' 3'2'9 fok ,o >kldNhl taldldr yrialv j¾.M,h  Wi" f,i f.k
mßudj .Kkh lrhs'
15' 3'2'10 >kldNhl § we;s ñkqï w;ßka yrialv j¾.M,h fidhd mßudj
.Kkh lrhs'
16' 3'2'11 yrialv j¾.M,h j¾. fikaáógrj,ska yd È. fyda Wi fikaáógr
j,ska § we;s >kldNhl mßudj .Kkh lrhs'
17' 3'2'12 yrialv j¾.M,h j¾. fikaáógrj,ska yd È. fyda Wi ógrj,ska §
we;s >kldNhl mßudj .Kkh lrhs'
3'3 ;%sfldaK m%siauhl mßudj
18' 3'3'1 ñkqï § we;s ´kE u RcqfldaKsl ;%sfldaKhl j¾.M,h .Kkh lrhs'
19' 3'3'2 fok ,o ´kE u ;%sfldaKhl" wdOdrlh yd ,ïn Wi u`.ska j¾.M,h
.Kkh lrhs'
20' 3'3'3 ;%sfldaK m%siauhl taldldr yrialv w÷re lr fmkajhs'
21' 3'3'4 yrialv yevh wkqj m%siau kï lrhs'
22' 3'3'5 RcqfldaKsl ;%sfldaK m%siauhl yrialv j¾.M,h .Kkh lrhs'
23' 3'3'6 RcqfldaKsl ;%sfldaK m%siauhl mßudj .Kkh lrhs'
24' 3'3'7 § we;s ñkqï weiqßka" ;%sfldaK m%siauhl yriallv j¾.M,h .Kkh
lrhs'
1 cm3
1 cm
1 cm

25' 3'3'8 ;%sfldaK m%siauhl mßudj .Kkh lrhs'
26' 3'3'9 ;%sfldaK m%siauhl mßudj yd yrialv j¾.M,h § we;s úg tys Wi
.Kkh lrhs'
27' 3'3'10 ;%sfldaK m%siauhl mßudj iu. Wi fyda È. ÿka úg tys yrialv
j¾.M,h .Kkh lrhs'
28' 3'3'11 Rcq m%siau we;=<;a .eg¨ úi|hs'



mßudj
wkdjrK mÍlaIKh
m%Yak m;%h'
1' my; oelafjk j.=fõ tla tla y÷kajdfok ku wh;a jk ;Srej f;dard o"
wfkla ;Srhg o fhdokak'
y÷kajdfok ku ;, rEmhls >kjia;=jls
iup;=ri%h
>klh
>kldNh
RcqfldaKdi%h
jD;a;h
is,skavrh
f.da,h
iudka;rdi%h
;%sfldaKh
2' my; oelafjk j.=fõ ±lafjk tla tla øjH wjldYfha .kakd bv ms<sn|j"
.e,fmk ;Srefõ ,l=K o " wfkla ;Srefõ ,l=K o fhdokak'
y÷kajdfok ku wjldYfha wjldYfha
bvla .kshs' bvla fkd.kshs'
.fvd,a legh
lvodish
fnda,h
ud¿ ákatl
úiaflda;= fmÜáh
íf,aâ ;,h
fmd;
ulklE,a,
3' my; j.=fõ ±lafjk >k jia;=j, yevh y÷kajk ku ,shkak'
>kjia;=j yevh y÷kajk ku
 
 
 

>k jia;=j yevh y÷kajk ku
iv
v
vi
4' my; oelafjk j.=fõ >klj, § we;s ñkqï weiqßka j.=j iïmQ¾K lrkak'
>klh >klfha me;a;l È.
1 cm
1 cm
1 cm
1 cm
2 cm
2 cm
2 cm
2 cm
3 cm
3 cm
3 cm
3 cm
5' my; >kldNj, § we;s ñkqï wkqj " my; oelafjk j.=j iïmQ¾K lrkak'
>kldNh È. m<, Wi
2 cm
1 cm
1 cm
2 cm
1 cm
3 cm
1 cm
4 cm
2 cm

6' fuu >kl yev;s legfha mßudj >kfikaá óg¾ 1 f,i i,ld
my; oelafjk tla tla >kldNj, mßudj we;=<;a lrñka j.=j
iïmQ¾K lrkak'
>kldNh È. m<, Wi leg .Kk mßudj
2cm 1cm 1cm
3cm 1 cm 1cm
3cm 2cm 1cm
1 cm3
7' my; j.=fõ ±lafjk ñkqï wkqj j.=j iïmQ¾K lrkak '
>kldNfha ñkqï >kldNfha mßudj
È. m<, Wi È. m<, Wi mßudj
i. 1cm 1cm 1cm 111 1 cm3
ii. 2cm 1cm 1cm
iii. 2cm 2cm 1cm
iv. 5cm 2cm 1cm
v. 8cm 5cm 1cm
8' oS we;af;a >kldNhkaf.a ñkqï h' tajdg wkqj j.=j iïmQ¾K lrkak'
i. 5cm 4cm 1cm 541 20 cm3
ii. 10cm 4cm 5cm
iii. 8cm 7cm 10cm
iv. 12cm 8cm 10cm
9' oS we;af;a >kldNhkaf.a ñkqï h' tajdg wkqj j.=j iïmQ¾K lrkak'
i. 5m 2m 1m 521 10 cm3
ii. 4m 2m 2 m
iii. 10m 5 m 3m
iv. 8 m 5 m 4 m
v. 12m 8 m 4 m
 
 
 

10' my; j.=fõ ±lafjkafka >kldNhl ñkqï h' tla tla >kldNj, ñkqï
weiqßka j.=j iïmQ¾K lrkak'
me;a;l È. me;a;l È.  me;a;l È. me;a;l È. mßudj
3 cm 3  3  3 27 cm3
5 cm
10 cm
12 cm
20 cm
11' my; oelafjk tla tla >k jia;=j ksÍlaIKh lsÍfuka " tys w÷re lr we;s
yrialv Bg iudka;r j w¢k ,o ´kE u ;,hl yrialvg m%udKfhka yd
yevfhka iudk jk fyda fkdjk nj wkqj j.=j iïmQ¾K lrkak'
>k jia;=j yrialv" m%udKfhka yrialv" m%udKfhka
yd yevfhka iudk h' yd yevfhka wiudk h'
i.
ii.
iii.
iv.
v.
12' my; oelafjk j.=j fyda fhdoñka iïmQ¾K lrkak'
>kjia;=j taldldr yrialvla ;sfí' taldldr yrialvla ke;'
>klh
>kldNh
iup;=ri% ms%iauh
;%sfldaK ms%iauh
fla;=j
is,skavrh

 
 
 

13' my; oelafjk tla tla >kldNfha w÷relr fmkajd we;s yrialv j¾.M,h
fidhkak'
>kldNh yrialv j¾.M,h
i.
2 cm
3 cm
5 cm
ii.
5 cm
4 cm
3 cm
iii. 10 cm
2 cm
5 cm
my; oelafjk A,B,C,D >kldN weiqßka m%Yak 14 yd 15 ys j.= iïmQ¾K
lrkak'
14' >kldNh È. m<, Wi mßudj
i. A 5 cm 2cm 2 cm 3
(2 2) 5 20cm  
ii. B 8cm 6 cm 10cm ...................= ........... cm3
iii. C ..... ..... ..... ...................= ........... cm3
iv. D .... .... ..... ...................= ........... cm3
...................= ........... cm2
...................= ........... cm2
...................= ........... cm2
2 cm
2 cm
5 cm
8 cm
6 cm
10cm
5 cm
5 cm
5 cm
5 cm
12 cm
2 cm
8 cm
A B C
D
w÷re l< fldgfia j¾.M,h


15' >kldNh yrialv j¾.M,h Wi$È. mßudj =
yrialv j¾.M,hWi
i. A 22 = 4 cm2
5 cm 4  5 = 20 cm3
ii. B 8  6 = ....... 10 cm ......................................
iii. C ..............= ........ 5 cm .....................................
iv. D ..............= ........ 12 cm .....................................
16' yrialv j¾.M,h yd Wi fyda È. § we;s my; j.=fõ oelafjk tla tla
>kldNj, mßud fidhd j.=j iïmQ¾K lrkak'
yrialv j¾.M,h Wi fyda È. mßudj
2 3
40 cm 12 cm 40 12 = 480 cm
2 3
10 cm 8 cm ............= ....... cm
2 3
25 cm 3 cm .............= ........ cm
2 3
100 cm 24 cm .......... = ........ cm
17' yrialv j¾.M,h yd Wi fyda È. § we;s my; oelafjk j.=fõ tla tla
>kldNj, mßudj we;=<;a lrñka j.=j iïmQ¾K lrkak'
yrialv j¾.M,h Wi fyda È. mßudj
10 m2
5 m 3
10 5 50m 
6 m2
4 m ............................
20 m2
12 m ............................
18 m2
10 m ............................
18' my; oelafjk tla tla RcqfldaKS ;%sfldaKj, j¾.M, we;=<;a lrñka j.=j
iïmQ¾K lrkak'
RcqfldaKS ;%sfldaKh j¾.M,h
1
2
 wdOdrlh ,ïn Wi
i.
10 cm
8 cm
21
10 8 40
2
cm  
ii.
6 cm
8 cm
10 cm
...............................................

RcqfldaKS ;%sfldaKh j¾.M,h
1
2
 wdOdrlh ,ïn Wi
iii.
4 cm
10 cm
.....................................................
iv.
5 cm
12 cm
13 cm
....................................................
19' my; oelafjk tla tla ;%sfldaKj, j¾.M, fidhd j.=j iïmQ¾K lrkak'
;%sfldaKh
1
2
wdOdrl mdofha È. ,ïn Wi = j¾.M,h
i. 5 cm 4 cm
10 cm
21
10 4 20
2
cm  
ii.
12 cm
5 cm
21
....... ....... ..............
2
cm  
iii. 6 cm
10 cm
5 cm
..............................................
iv.
12 cm
6 cm
7 cm
..............................................



20'my; oelafjk tla tla ;%sfldaK m%siaufha taldldr yrialv w÷re lrkak'
21' my; oelafjk tla tla Rcq m%siauh" tys yrialv wkqj kï lrñka ysia;eka
iïmQ¾K lrkak'
i. RcqfldaKS ;%sfldaK yrialvla iys; Rcq m%siauhls'
ii. '''''''''''''''''''''''''''''''''''''''' yrialvla iys; Rcq m%siauhls'
iii. '''''''''''''''''''''''''''''''''''''''' yrialvla iys; Rcq m%siauhls'
iv. '''''''''''''''''''''''''''''''''''''''' yrialvla iys; Rcq m%siauhls'
22' my; oelafjk tla tla RcqfldaKS ;%sfldaK m%siaufha yrialv j¾.M,h" § we;s
ysia;eka iïmQ¾K lrñka ,nd .kak'
5 cm
3 cm
4 cm
(i.) (ii.) (iii.)
(iv.)
yrialv j¾.M,h
2
1
....... .......
2
..............cm
  


ii.
6 cm
8 cm
14 cm
10 cm
iii.
5 cm
12 cm
13 cm
15 cm
23' 22 m%Yakfhys we;=<;a (i) , (ii), (iii) ;%sfldaK m%siauj, mßudj my; ysia;eka
iïmQ¾K lrñka ,nd.kak'
i. mrsudj = yrialv j¾.M,h È.
= ............. x ............
= ............... cm3
ii.
iii.
24' my; oelafjk tla tla ;%sfldaK m%siauj, yrialv j¾.M,h § we;s ysia;eka
iïmQ¾K lrñka ,nd .kak'
i.
10 cm
8 cm
6 cm
ii.
10 cm
12 cm
4 cm
yrialv j¾.M,h
2
1
....... .......
2
..............cm
  

yrialv j¾.M,h
2
1
....... .......
2
..............cm
  


xmrsudj = yrialv j¾.M,h È.
= ............. x ............
= ............... cm3
mrsudj = yrialv j¾.M,h È.
= ............. x ............
= ............... cm3
yrialv j¾.M,h
2
1
...... ........
2
.................cm
  

yrialv j¾.M,h
2
1
...... ........
2
.................cm
  


iii.
20 cm
8 cm
12 cm
25'24 m%Yakfha oelafjk tla tla m%sfldaK m%siauj, mßudj my; § we;s ysia;eka
iïmQ¾K lrñka ,nd.kak'
i. ;s%fldaK m%siaufha mßudj
3
........ ..........
.................cm

 

ii. ;s%fldaK m%siaufha mßudj
3
........ ..........
.................cm

 

iii. ;s%fldaK m%siaufha mßudj
3
........ ..........
.................cm

 

26' my; oelafjk j.=fõ § we;s ;%sfldaK m%siauj,g wod< f;dr;=rej,g wkqj tys
ysia;eka iïmQ¾K lrkak'
mßudj yrialv j¾.M,h È. ,nd.kakd wdldrh È.
i. 200 cm3
40 cm2
200
40 5 cm
ii. 120 cm3
30 cm2 .................................................... ........................
iii. 48 cm3
12 cm2 ................................................... .........................
iv. 220 cm3
20 cm2 .................................................. ........................
yrialv j¾.M,h
2
1
...... ........
2
.................cm
  

yrialv j¾.M,h Wi

27' my; oelafjk j.=fõ § we;s ;%sfldaK m%siauj,g wod< f;dr;=rej,g wkqj tys
ysia;eka iïmQ¾K lrkak'
mßudj È. yrialv j¾.M,h yrialv j¾.M,h
,nd.kakd wdldrh
400 cm3
5 cm
400
5 80 cm2
140 cm3
4cm .............................. .................................
900 cm3
5 cm .............................. ..................................
1400 cm3
10 cm .............................. ..................................
28' my; oelafjk tla tla Rcq m%siauj,g wod<j W;a;r imhkak'
i. iup;=ri% Rcq m%siauhl mßudj 768 cm3
o" Wi 12 cm o fõ'
(a) m%siaufha yrialv j¾.M,h fidhkak'
(b) m%siaufha yrialv me;a;l È. fidhkak'
ii. RcqfldaKS ;%sfldaK m%siauhl mßudj 120 cm3
fõ'
(a) m%siaufha È. 10 cm kï yrialv j¾.M,h fidhkak'
(b) yrialv" RcqfldaKh wvx.= tla mdohla 6 cm kï wfkla mdofha È.
fidhkak'
iii. RcqfldaKdi% m%siauhl mßudj 960 cm3
fõ ' tys Wi 12 cm kï"
(a) m%siaufha yrialv j¾.M,h fidhkak'
(b) yrialv È. 10 cm kï m<, fidhkak'

mßudj
wkdjrK mÍlaIKh
W;a;r yd Wmfoia
1' ;, rEmhls >kjia;=jls
>klh
>kldNh
RcqfldaKdi%h
jD;a;h
is,skavrh
f.da,h
iudka;rdi%h
;%sfldaKh
2'
.fvd,a legh
lvodish
fnda,h
ud¿ áka tl
úiaflda;= fmÜáh
íf,aâ ;,h
fmd;
ulk lE,a,
3. i. iv
ii. v.
iii. vi.
4. i. 1cm ii. 2cm iii. 3cm
5.
i. 2cm 1cm 1cm
ii. 3cm 1cm 2cm
iii. 4cm 2cm 1cm
6. i. 2,2cm3
ii. 3,3cm3
iii. 6,6cm3
7. ii
iii. 3
2 2 1 4cm  
iv. 3
5 2 1 10cm  
v. 3
8 5 1 40cm  
8. ii. 3
10 4 5 200cm  
iii. 3
8 7 10 560cm  
iv. 3
12 8 10 960cm  
























>klh fla;=j
>kldNh ;%sfldaK m%siauh
is,skavrh p;=ia;,h
È. m<, Wi








3
2 1 1 4cm  

9. ii. 3
4 2 2 16m  
iii. 3
10 5 3 150m  
iv. 3
8 5 4 160m  
v. 3
12 8 4 384m  
10. ii. 3
5 5 5 125cm  
iii. 3
10 10 10 1000cm  
iv. 3
12 12 12 1728cm  
v. 3
20 20 20 8000cm  
11. ii.
iii.
iv.
v.
12. ii.
iii.
iv.
v.
vi.
13. i. 2
3 2 6cm 
ii. 2
4 3 12cm 
iii. 2
5 2 10cm 
14. ii. 3
8 , 6 ,10 ; (8 6) 10 480cm cm cm cm  
iii. 3
5 , 5 , 5 ; (5 5) 5 125cm cm cm cm  
iv. 3
12 ,8 , 2 ;(8 2) 12 192cm cm cm cm  
15. ii. 2 3
8 6 48 ; 48 10 480cm cm   
iii. 2 3
5 5 2 5 ; 2 5 5 1 2 5c m cm   
iv. 2 3
8 2 1 6 ;1 6 1 2 1 9 2cm cm   
16. ii. 3
1 0 8 8 0 cm 
iii. 3
2 5 3 7 5cm 
iv. 3
1 00 2 4 2 40 0cm 
17. ii. 3
6 4 2 4 m 
iii. 3
20 12 240m 
iv. 3
1 8 1 0 1 8 0 m 
18. ii. 21
8 6 24
2
cm   iii. 21
10 4 20
2
cm   iv. 21
12 5 30
2
cm  
19. ii. 2
30512
2
1
cm iii. 2
25510
2
1
cm iv.. 2
36612
2
1
cm







>kldNh
iup;=ri% msrñvh
;%sfldaK m%siauh
fla;=j
is,skavrh











20.
21. ii.
iii.
iv.
22. i.
21
4 3 6
2
cm  
ii.
21
6 8 24
2
cm  
iii.
21
5 12 30
2
cm  
23. i. 3
6 5 30cm 
ii. 3
24 14 336cm 
iii. 3
30 15 450cm 
24. i.
21
10 6 30
2
cm  
ii.
21
4 12 24
2
cm  
iii.
21
20 8 80
2
cm  
25. i. 3
3 0 8 2 4 0 cm 
ii. 3
24 10 240cm 
iii. 3
80 12 96 0cm 
26. ii.
120
4
30
cm
iii.
48
4
12
cm
iv.
220
11
20
cm
27. ii.
2140
35
4
cm
iii.
2900
180
5
cm
iv.
21400
140
10
cm
iup;=ri%
RcqfldaKdi%
iuoaùmdo ;%sfldaK
wjidk W;a;rhg kshñ;
tall wjYH hs'

4' jD;a;hl j¾.M,h
ld¾h úYaf,aIKh
4'1 jD;a;hl ,laIK
4'2 jD;a;fha j¾.M,h
4'3 jD;a;hl j¾.M,h wdY%s; fhÿï

jD;a;hl j¾.M,h
wkdjrK mÍlaIKh
m%Yak wruqKq wruqKq
wxlh wxlh
4'1 jD;a;hl ,laIK
1' 4'1'1 jD;a;hl wrh y÷kd .kshs'
2' 4'1'2 jD;a;hl wrh § we;s wlaIrh weiqßka kï lrhs'
3' 4'1'3 jD;a;hl wrh kï lr ,shd olajhs'
4' 4'1'4 jD;a;hl úIalïNh yd mßêh w;r wkqmd;h ±laùug  ixfla;h
fhdod .kshs'
5' 4'1'5  ys w.h
7
22
hkak Ndú; lrhs'
6' 4'1'6  ys w.h oYu ia:dk follg ksjerÈj 3'14 hkak Ndú; lrhs'
4'2 jD;a;fha j¾.M,h
7' 4'2'1 wrh r jQ jD;a;hl j¾.M,h 2
r nj m%ldY lrhs'
8" 9" 4'2'2 wrh ÿka úg jD;a;fha j¾.M,h fiùug 2
r hkafkys" wrfha w.h
wdfoaY lrhs'
10"11 4'2'3 wrfha w.h 2
r hkafkys wdfoaY lr jD;a;fha j¾.M,h fidhhs'
12"13
14' 4'2'4 j¾.M,h ÿkaúg jD;a;fha wrh .Kkh lrhs'
4'3 jD;a;hl j¾.M,h wdY%s; fhÿï
15' 4'3'1 RcqfldaKdi%hlska jD;a;hla bj;a l<úg ,efnk b;sß fldgfia
j¾.M,h .Kkh lrhs'
16' 4'3'2 jD;a;hlska RcqfldaKdi%hla bj;a l< úg ,efnk b;sß fldgfia
j¾.M,h .Kkh lrhs'
17' 4'3'3 RcqfldaKS iuoaùmdo ;%sfldaKhlska jD;a;hla lmd bj;a l< úg
,efnk b;sß fldgfia j¾.M,h .Kkh lrhs'
18' 4'3'4 jD;a;hlska tal flakaøsl jD;a;hla bj;a l< úg ,efnk b;sß
fldgfia j¾.M,h .Kkh lrhs'
19' 4'3'5 jD;a;hl j¾.M,h yd tu jD;a;fha wrh fuka fo.=Khl wrhla
iys; jD;a;hl j¾.M,h w;r wkqmd;h fidhhs'

4' jD;a;hl j¾.M,h
wkdjrK mÍlaIKh
m%Yak m;%h
1' jD;a;hl wrh ±lafjk rEmh háka brla w¢kak'
i.
ii.
iii.
2' jD;a;fha wrh ±lafjk bx.%Sis wlaIrh ;s;a br u; ,shkak'
i.
....................
ii.
....................
iii.
....................
. . .
. . .
.. .
.a .
b
.c
.
x
.
z
.y
.p .
q
.
r

3' jD;a;hl wrh ksrEmKh jk f¾Ld lKavh ;s;a br u; ,shkak '
i.
....................
ii.
....................
iii.
....................
4' jD;a;hl mrêh yd úIalïNh w;r wkqmd;h ±lafjk ixfla;h háka brla
w¢kak'
i. (a)  (b)  (c) 
ii. (a)  (b)  (c) 
iii. (a)  (b)  (c) 
5' jvd;a ksjeros m%ldYh háka brla w¢kak'
jD;a;hl mßêh yd úYalïNh w;r wkqmd;h jkqfha "
i. (a) 7
22
(b) 22
7
(c) 3
22
ii. (a) 3
1
(b) 7
22
(c) 5
22
iii. (a) 6
7
(b) 7
22
(c) 22
7
6' jvd;a ksjeros m%ldYh háka brla w¢kak'
jD;a;hl mßêh yd úIalïNh w;r wkqmd;h oYu ia:dk follg ,shQ úg w.h
jkqfha "
i. (a) 3.72 (b) 3.21 (c) 3.14
ii. (a) 3.24 (b) 3.14 (c) 3.34
iii. (a) 3.17 (b) 3.61 (c) 3.14
.
A
B
.
C
D
O
.O
.
A O
.
O
K .O
D
.O .O
.O
S
R
M
E
F
hs' hs' hs'
hs' hs' hs'
hs' hs' hs'
hs' hs' hs'
hs' hs' hs'
hs' hs' hs'

7' jvd;a ksjerÈ m%ldYh háka brla w¢kak'
i. wrh s jQ jD;a;hl j¾.M,h jkqfha "
(a) s2 (b) 2
2 s (c) 2
s
ii. wrh t jQ jD;a;hl j¾.M,h jkqfha "
(a) 2
2 t (b) 2
t (c) t
iii. wrh r jQ jD;a;hl j¾.M,h jkqfha "
(a) 2
r (b) 22
r (c) 2
2 r
8' ksjerÈ m%ldYh háka brla w¢kak'
i. wrh 6 cm jQ jD;a;hl j¾.M,h ±lafjkqfha "
(a)
2
6
7
22
cm (b)
2
66 cm (c)
2
66
7
22
cm
ii. wrh 8 cm jQ jD;a;hl j¾.M,h ±lafjkqfha "
(a) 8
7
22
 (b) 88
7
22
 (c) 888
7
22

iii. wrh 5.5 cm jQ jD;a;hl j¾.M,h ±lafjkqfha "
(a) 5.55.5
7
22
 (b) 25.5
7
22
 (c) 5.5
7
22
2 
9' A fldgfiys wrh § we;s jD;a;j, j¾.M," B fldgiska f;dard hdlrkak'
jD;a;fha wrh jD;a;fha j¾.M,h
r 55
7
22

p 33
7
22

3 rr 
7
22
5 77
7
22

7 pp
7
22
h' h' h'
h' h' h'
h' h' h'
hs' hs' hs'
hs' hs' hs'
hs' hs' hs'

10' ksjerÈ W;a;rh háka brla w¢kak'
i. wrh 7 cm jQ jD;a;hl j¾.M,h jkqfha"
(a) 145 cm2
(b) 44 cm2
(c) 154 cm2
ii. wrh 14 cm jQ jD;a;hl j¾.M,h jkqfha"
(a) 716 cm2
(b) 616 cm2
(c) 666 cm2
iii. wrh 21 cm jQ jD;a;hl j¾.M,h jkqfha"
(a) 1386 cm2
(b) 1586 cm2
(c) 1366 cm2
i. wrh 10.5 cm jQ jD;a;hl j¾.M,h jkqfha"
(a) 864.5 cm2
(b) 962.5 cm2
(c) 346.5 cm2
ii. wrh 3.5 cm jQ jD;a;hl j¾.M,h jkqfha"
(a) 38.5 cm2
(b) 83.5 cm2
(c) 36.6 cm2
iii. wrh 17.5 cm jQ jD;a;hl j¾.M,h jkqfha"
(a) 692.5 cm2
(b) 962.5 cm2
(c) 926.5 cm2
12' § we;s f;dr;=re wkqj j¾.M,fhka iudk rEmj, wlaIr ;s;a br u;
,shkak'
''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
.
a
14cm .
b
21cm .
c
14cm .
d
35 cm .
e
20 cm .
f
28 cm
h' h' h'
h' h' h'
h' h' h'
h' h' h'
h' h' h'
h' h' h'
13' § we;s f;dr;=re wkqj ta ta jD;a;hg wh;a wrh" A fldgqj ;=<ska f;dard
hd lrkak'
A
j¾.M,h jD;a;fha wrh
3.5 cm
962.5 cm2
7.5 cm
346.5 cm2
10.5 cm
38.5 cm2
12.5 cm
17.5 cm

rEmfha ±lafjk wdldrhg RcqfldaKdi%hlska
jD;a;dldr fldgila bj;alr we;'
(a) È. 25 cm yd m<, 20 cm jk RcqfldaKdi%fhka wrh 7 cm jQ jD;a;hla
lmd bj;a l< úg b;sß jk fldgfia j¾.M,h jkqfha "
i. 154 cm2
ii. 346 cm2
iii. 355 cm2
(b) È. 10 cm yd m<, 8 cm jk RcqfldaKdi%fhka wrh 3.5 cm jQ jD;a;hla
lmd bj;a l< úg b;sß jk fldgfia j¾.M,h jkqfha "
i. 80 cm2
ii. 38.5 cm2
iii. 41.5 cm2
(c) È. 30 cm yd m<, 25 cm jk RcqfldaKdi%fhka wrh 10.5 cm jQ
jD;a;hla lmd bj;a l< úg b;sß jk fldgfia j¾.M,h jkqfha "
i. 346.5 cm2
ii. 403.5 cm2
iii. 750 cm2
rEmfha ±lafjk wdldrhg jD;a;hlska
iup;=ri%hla lmd bj;alr we;'
(a) wrh 10.5 cm jk jD;a;hlska" me;a;l È. 8.5 cm jk iup;=ri%hla lmd
bj;a l< úg b;sß jk fldgfia j¾.M,h jkqfha "
i. 346.5 cm2
ii. 72.25 cm2
iii. 274.25 cm2
h' h' h'
h' h' h'
h' h'
h'
h' h' h'
14' § we;s f;dr;=re wkqj ta ta jD;a;hg wh;a j¾.M,h " B fldgqj ;=<ska f;dard
hd lrkak'
B
316 cm2
536 cm2
1386 cm2
786 cm2
154 cm2
274 cm2
. 21 cm
. 14 cm
. 7 cm

(b) wrh 7 cm jk jD;a;hlska" me;a;l È. 5 cm jk iup;=ri%hla lmd bj;a l<
úg b;sß jk fldgfia j¾.M,h jkqfha "
i. 129 cm2
ii. 25 cm2
iii. 154 cm2
(c) wrh 14 cm jk jD;a;hlska" me;a;l È. 10 cm jk iup;=ri%hla lmd bj;a
l< úg b;sß jk fldgfia j¾.M,h jkqfha "
i. 716 cm2
ii. 616 cm2
iii. 516 cm2
rEmfha ±lafjk wdldrfha RcqfldaKsl"
iuoaùmdo ;%sfldaKhlska jD;a;hla lmd
bj;afldg we;'
(a) RcqfldaKh wvx.= mdohl È. 20 cm jk iuoaùmdo RcqfldaKsl
;%sfldaKhlska" wrh 3.5 cm jk jD;a;hla lmd bj;a l< úg b;sßjk
fldgfia j¾.M,h jkqfha "
i. 38.5 cm2
ii. 261.5 cm2
iii. 161.5 cm2
(b) RcqfldaKh wvx.= mdohl È. 30 cm jk iuoaùmdo RcqfldaKsl
;%sfldaKhlska" wrh 7 cm jk jD;a;hla lmd bj;a l< úg b;sßjk
i. 256 cm2
ii. 296 cm2
iii. 746 cm2
(c) RcqfldaKh wvx.= mdohl È. 35 cm jk iuoaùmdo RcqfldaKsl
;%sfldaKhlska" wrh 10.5 cm jk jD;a;hla lmd bj;a l< úg b;sßjk
i. 266 cm2
ii. 328 cm2
iii. 909 cm2
rEmfha ±lafjk wdldrhg talflakaøsl jD;a;
folla we| " we;=<; jD;a;h lmd bj;afldg we;'
(a) wrh 17.5 cm jk jD;a;hlska" wrh 7 cm jk jD;a;hla lmd bj;a l< úg
b;sß jk fldgfia j¾.M,h jkqfha "
i. 625.5 cm2
ii. 962.5 cm2
iii. 808.5 cm2
(b) wrh 14 cm jk jD;a;hlska" wrh 10.5 cm jk jD;a;hla lmd bj;a l< úg
i. 962 cm2
ii. 870 cm2
iii. 269.5 cm2
h' h' h'
h' h' h'
h' h' h'
h' h' h'
h' h' h'
h' h' h'
h' h' h'

(c) wrh 14 cm jk jD;a;hlska" wrh 7 cm jk jD;a;hla lmd bj;a l< úg
i. 770cm2
ii. 462 cm2
iii. 562 cm2
19' (a) wrh r jQ jD;a;hl j¾.M,h " tu jD;a;fha wrh fuka fo.=Khla wrh we;s
jD;a;hl j¾.M,hg ork wkqmd;h jkqfha"
i. 1:1 ii. 1:2 iii. 1:4
(b) wrh 2a jQ jD;a;hl j¾.M,h " tu jD;a;fha wrh fuka fo.=Khla wrh we;s
i. 1:2 ii. 1:4 iii. 2:16
(c) wrh 3t jQ jD;a;hl j¾.M,h " tu jD;a;fha wrh fuka fo.=Khla wrh we;s
i. 1:4 ii. 1:2 iii. 3:6h' h' h'
h' h' h'
h' h' h'
h' h' h'

4' jD;a;hl j¾.M,h
wkdjrK mÍlaIKh
W;a;r yd Wmfoia
W;a;r Wmfoia
1. i. .
ii. .
iii. .
2. i. .a
ii. .
q
a q
iii. .
z
z
3. i. CO , OD ii. OM
iii. OD
4. i. (b) ii. (c) iii. (a)
5. i. (a) ii. (b) iii. (b)
6. i. (c) ii. (b) iii. (c)
7. i. (c) ii. (b) iii. (a)
8. i. (c) ii. (b) iii. (a)
9. r 55
7
22

p 33
7
22

3 rr 
7
22
5 77
7
22

7 pp
7
22
10. i. (c) ii. (b) iii. (a)
11. i. (c) ii. (a) iii. (b)
12. a, c, f
13. 3.5cm
962cm2
7.5cm
346.5cm2
10.5cm
38.5cm2
12.5cm
17.5cm
rEmh háka brla we£u fyda ksjerÈ
rEmh y÷kd .ekSug yels jk
i,l=Kla fh§u'
CO fyda OD fh§u m%udKj;a h'
OC,MO fyda DO ;sìh yels h'

14. 21 cm 616 cm2
536 cm2
14cm 1386 cm2
786 cm2
7 cm 154 cm2
274 cm2
15. (a) ii. (b) iii. (c) ii
16. (a) iii. (b) i. (c) iii
17. (a) ii (b) ii. (c) i.
18. (a) iii. (b) iii. (c) ii.
19. (a) iii. (b) ii. (c) i.

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