3. Mensuration
•What Is Meant By Area
A Figure Made up Of Straight Line Segment Called A Rectilinear Figure
The Surface Of the Boundary Is Called Area
4. AREA OF RECTANGLE
• Rectangle
Area=l x b
Perimeter = 2(l+b)
Mensuration
Where As l=Length
b=Breadth
N l O
b
M P
d
5. AREA OF SQUARE
• Area Of Square =S2
• Perimeter Of Square = 4 x S
Mensuration
Here S is the Side of the square
S
S
6. EXAMPLES
• Ex.1 Show That Area Of a Square =
1
2
x Diagnoal 2
.find the Area Of Square Whose Diagonol Is = 2.5
cm
• In Right Angle Triangle BCD
• Diagonal2 =DC2 + CB2 = S2+S2=2S2
• But The Area Of Square = S2
• Diagonal2=2 x Area
• Area = =
1
2
x Diagnoal 2
Mensuration
A S B
S
C
D
7. • If Diagonal = 2.5
• Area = =
1
2
x 2.5 2
• =
1
2
x 6.25
• Ans- 3.125
Mensuration
If we take 2 to left side we get ,
Area =
1
2
x Diagnoal 2
2nd Case
8. • Ex-2 the Length And Breadth Of a rectangular Field Is in the
ratio of 4:3 if the area is 3072 m2 find the cost of fencing
the field at the rate of 4 rupees Per meter
• Let the Length And Breadth Be 4x and 3x
• Area Of field = l x b
• 4𝑥 𝑋 3𝑥 = 12𝑥 2 = 3072
• Hence x = 16
Mensuration
9. • Length = 4x= 64m , breadth = 3x = 48m
• Length of fencing = Perimeter of the field
• 2(64+48)
• =224m
• Cost Of Fencing = 4(224)m
• = R896
Mensuration
10. Mensuration
AREA OF PARALLELOGRAM
A B
D E C
Consider Parallelogram ABCD.
Let AC Be the Diagonal
In ADC And CBA
AD=CB, CD=AB
AC is the common
ADC = CBA
Area Of Parallelogram ABCD
=Area of ADC + Area Of ABC]
= 2 x Area Of ADC
=2 x (1/2 CD x AE) (Where AE|DC)
= DC x AE
i.e. Area Of Parallelogram = Base x Height
11. AREA OF RHOMUS
• Since rhombus is a parallelogram its area is given by
• Area Of rhombus = Base x Height
• Area Of Rhombus ABCD = Area Of ABD +Area of CBD
• => ½(BD x AO) + ½(BD x CO)
• => ½(BD(AO+CO))
• => ½ BD+AC
• i.e. Area Of Rhombus = ½ x diagonals = ½ (d1 x d2)
Mensuration
O
A
B
D C
12. AREA OF TRAPEZIUM
• Let ABCD be a Trapezium With AB || DC.
Draw AE and BF Perpendicular to DC
• Then AE=BF= height of trapezium =
h
• Area of trapezium ABCD = Area of ADE +
Area of rectangle ABFE + Area of BCF
Mensuration
A B
D E F
C
13. • ½ x DE x h + EF x h + ½ FE x h
• ½ h(DE+2EF + FC )
• ½ h(DE+EF+FC+EF)
• ½ h (DC+EF)
• ½ h(DC+AB) ( as EF = AB)
• i.e. Area of trapezium = ½ x sum of the parallel lines x Distance
Between Parallel Sides
Mensuration
A B
D E F
C
14. AREA OF
QUADRILATERAL
• Let ABCD be a Quadrilateral and AC be one of
its diagonal. Draw Perpendicular BE and DF
From B and D respectively to AC
• Area of Quadrilateral ABCD
Area Of ABC + Area of ADC
½ AC x BE + ½ AC x DF
½ AC(BE +DF )
If AC = d , BE = h1 , DF = h2 then
Area Of Quadrilateral = ½ d(h1+h2)
Mensuration
D
F
E
21. A SPECIAL THANKS TO MY
TEACHERS
Mensuration
Things I used in this ppt
1. An Olympiad book for questions
2. PPT Presentation
3. Reference books and my Brain for Matter
4. 3d Painter For Shapes
