The document contains a series of geometric problems related to triangular, rectangular, square, pentagonal, and hexagonal laminae, detailing their projections and positions with respect to horizontal and vertical planes. Each problem includes specific dimensions, orientations, and solution approaches prepared by Raghavendra T. Anegundi. The document serves as a guide for understanding the projection methods used in technical drawing and geometry.

1. Problem 01: An equilateral triangular lamina of 25mm side lies with one of its edges on HP such
Solution:
Problem 02: A triangular plane figure of sides 25mm is resting on HP with one of its corners,
position.
Solution:
Problems on Triangular lamina
Page No. 01
X Y
VP
HP
a
b
c
25
a'b'(c')
FV
b'(c')
a'
a
b
c
DTV
a
b
c
a'
b'c'
FFV
TV
X Y
VP
HP
TV
FV
a
b
c
25
a' b'(c') a'
b'(c')
a
b
c
c
b
a
a'
b'c'
DTV
FFV
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE

2. Problem 03: A triangular plane lamina of sides 25mm is resting on HP with one of its corners
touching it, such that the side opposite to the corner on which it rests is 15mm above HP and
inclination of the lamina to the reference plane.
Solution:
Problem 04: An equilateral triangular lamina of 25mm sides lies with one of its side on HP. The
one of its medians
projections.( -method)
Solution:
Problem 05: A triangular lamina of 25mm sides rests on one of its corners on VP, such that the
median passing through corner
projections. ( -method)
Solution:
Page No. 02
X Y
VP
HP
a
b
c
25
a'b'(c') b'(c')
a'
b
c
ad d1
Locus of D
a
b
c
d1
a'
b'c'
DTV
FFV
TV
FV
d
X
VP
HP
a'
b'
c'
d'
a c(b)
Ya
c(b)
25
a'
b'
c'
d1'
DFV
Locus of D
a' b'
c'
d1'
a
c b
FTV
TV
FV
X Y
VP
HP
TV
FV
DTV
FFV
a
b
c
25
a' b'(c') a'
b'(c')
15
a
b
c
a
b
c
a'
c'
b'
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE

3. Problem 06: longest side is in
projections of the set-square.
Solution:
Problem 07: An isosceles triangular plate of negligible thickness has base 25mm long and altitude
35mm. It is so placed on HP such that in the front view it is seen as an equilateral triangle of 25mm
sides
determine the inclination of the plate with the reference plane.
Solution:
Page No. 03
X Y
VP
HP
TV
FV
DTV
FFV
60
a
b
c
b'(a') c' b'(a')
c'
a
b
c
a
b
c
c'
b'a'
X Y
VP
HP
TV
FV
25
b'
c'
a'
a(b) c
25
c'
b'
a'
a(b)
c
c'
a'
b'
c
ba
DFV
FTV
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE

4. Problems on Rectangular lamina
Problem 12: A rectangular lamina of sides 20mm x 30mm rests on HP on one of its longer edges.
Solution:
Problem 13: A rectangular lamina of sides 20mm x 30mm rests on VP on one of its longer edges.
Solution:
Page No. 04
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
FV
DTV
FFV
TV
30
20
a b
cd
a'(d') b'(c')
b'(c')
a'(d')
a b
cd
d
a
c
b
b'c'
d' a'
X
VP
HP
FV
TV
Y
DFV
FTV
30
20
a' b'
c'd'
a(d) b(c)
b(c)
a(d)
a' b'
c'd'
d'
a'
b'
c'
a
b c
d

5. Problem 15: A rectangular plate of negligible thickness of size 35mm x 20mm has one of its
shorter edges in VP front view is
square of side 20mm.
Solution:
Problem 14: A rectangular lamina of sides 35mm x 20mm rests on HP on one of its shorter edges.
The lamina is rotated about the edge on which it rests till it appears as a square in the top view.The
Solution:
Page No. 05
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
FV
DTV
FFV
TV
X
VP
HP
FV
TV
Y
FTV
20
35
a b
cd
a'(d') b'(c') a'(d')
b'(c')
a b
cd
d
a
b
c
b'
a'd'
c'
DFV
20
35
a' b'
c'd'
a(d) b(c) a(d)
b(c)
a' b'
c'd'
a
20
a'
d'
c'
b'
d
b c

6. Problems on Square lamina
Problem 08:
Solution:
Problem 09:
Solution:
Page No. 06
X Y
VP
HP
ab
c d
a'(d')b'(c')
b
c
a
d
b'(c')
a'(d')
c
b
a
d
a'
b'c'
d'
TV
FV
DTV
FFV
c
b
a
d
a'
b' c'
d'
OR
X Y
VP
HP
TV
FV
c
b
a
d
c' b'(d') a'
c a
b
d
c'
b'(d')
a'
DTV
a
dc
b
b
a
d
c
d'
c'
b'
a' FFV
d'
c'
b'
a'
OR
Prepared By
Raghavendra T. Anegundi

7. Problem 10: A square lamina of 40mm sides rests on HP such that one of the diagonals
projections.
Solution:
Problem 11: A square lamina of 40mm sides rests on VP such that one of the diagonals
projections.
Solution:
Page No. 07
X Y
VP
HP
TV
FV
FFV
a
b
c
d
a' b'(d') c'
a c
b
d
a'
b'(d')
c'
c c1
d
a
b Locus of C
d'
c'
b'
a'
Locus of Aa1 a
c
d
b
FFV
d'
c'
b'
a'
DTV
OR
X Y
VP
HP
TV
FV
a'
b'
c'
d'
a b(d) c a
b(d)
c
a' c'
b'
d'
DFV
FTV
c' c1'
d'
a'
b'
Locus of C
d
c
b
a
Locus of Aa1' a'
c'd'
b'
FTV
d
c
b
a
OR

8. Problems on Square & Rectangular lamina (On Profile Plane)
Problem 16: The top view of a square lamina of side 30mm is a rectangle of side 30mm x 20mm
with the longer side of the rectangle being parallel to both HP and VP. Draw the top and front
views of the square lamina. What is the inclination of the surface of the lamina with HP and VP.
Solution:
Problem 17: A rectangular lamina of 30mm x 20mm rests on HP on one of its shorter edges. The
lamina is rotated about the edge on which it rests till it appears as a square in the top view. The
edge on which the lamina rests being parallel to both HP and VP. Draw its projections and find its
inclinations to HP and VP.
Solution:
Page No. 08
X Y
VP
HP
FV
TV
30
a b
cd
a'(d') b'(c') a'(d')
b'(c')
a b
cd
30
20
X1
Y1
a d
cb
a' d'
c'b'
a''(d'')
b''(c'')
RPP (LSV)
DTV
FFV
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
FV
DTV
TV
20
35
a b
cd
a'(d') b'(c') a'(d')
b'(c')
a b
cd
b c
da
a' d'
b' c'
X1
Y1
RPP (LSV)
a''(d'')
b''(c'')
FFV

9. Page No. 09
Problem 18: A rectangular lamina of sides 20mm x 25mm has an edge in HP and adjoining edge
in VP, is tilted such that the front view appears as a rectangle of 20mm x 15mm.The edge,which is
in VP, is 30mm from the right profile plane. (a) Draw the top view, front view and left profile view
in this position. (b) Find its inclination with the corresponding principal planes.
Solution:
Problem 19: The front view of a rectangular lamina of sides 30mm x 20mm is square of 20mm
sides. Draw the projections and determine the inclinations of the surface of the lamina with HP and
VP.
Solution:
Problem 20: A mirror 30mm x 40mm is inclined to the wall such that its front view is a square of
30mm side. The longer sides of the mirror appears perpendicular to both HP and VP. Find the
inclination of the mirror with the wall
Solution:
X Y
VP
HP
FV
TV
X1
Y1
RPP (LSV)
25
20
a' b'
c'd'
d(a) c(b)
a' b'
c'd'
20
15
30
d(a)
c(b)
c''d''
b''a''
X
VP
HP
FV
TV
Y
30
20
a' b'
c'd'
a(d) b(c)
a' b'
c'd'
20
X1
Y1
a b
cd
a''(b'')
d''(c'')
RPP (LSV)
X
VP
HP
FV
TV
Y
30
40
a' b'
c'd'
d(a) c(b)
30
a' b'
c'd'
X1
Y1
d''(c'')
d''(c'')
a''(b'')
RPP (LSV)
a b
cd
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE

10. Problems on Pentagonal lamina
Page No. 10
Problem 21: A pentagonal lamina of the edges 25mm is resting on HP with one of its sides such
VP. Draw its projections.
Solution:
Problem 22: A pentagonal lamina of the edges 25mm is resting on VP with one of its sides such
HP. Draw its projections.
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
a
b
c
d
e
a'b'(e')c'(d')
25
a
b
c
d
e
a
bc
d
e
a' a'
b'(e')
c'(d')
b'
c'd'
e'
FFV
DTV
X Y
VP
HP
FV
TV
a'
b'
c'
d'
e'
ab(e)c(d)
25
a'
b'
c'
d'
e'
a
b(e)
c(d)
FTV
DFV
a'
b'
c'
d'
e'
a
b
c d
e

11. Page No. 11
Problem 23: A pentagonal lamina of the edges 25mm is resting on HP with one of its corners
corner on which the lamina rests make equal inclination with HP. When the edge opposite to this
the plane lamina in this position.
Solution:
Problem 24: A pentagonal lamina of the edges 25mm is placed on one of its corners on HP such
the top and front views of the lamina.
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X
VP
HP
TV
FV
FFV
DTV
a
b
c
d
e
a' b'(e') c'(d')
a'
b'(e')
c'(d')
a
b
c
d
e
Y
a
b c
d
e
a'
b'
c' d'
e'
25
X
VP
HP
TV
FV
FFV
DTV
Y
a
b
c
d
e
a' b'(e') c'(d')
25
a
b
c
d
e
a'
b'(e')
c'(d')
a'
b'
c' d'
e'
a
b
c
d
e
m m
m

12. Page No. 12
Problem 25: A pentagonal lamina of the edges 25mm is placed on one of its corners on VP such
the top and front views of the lamina.
Solution:
Problem 26: A pentagonal lamina having edges 25mm is placed on one of its corners on VP such
front views of the lamina.
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X
VP
HP
FV
TV
FTV
DFV
Y
a'
b'
c'
d'
e'
a b(e) c(d)
25
a'
b'
c'
d'
e'
a'
b'(e')
c'(d')
a
b
c d
e
m' m'
m'
a'
b'
c'
d'
e'
X
VP
HP
FV
TV
DFV
Y
a'
b'
c'
d'
e'
a b(e) c(d)
25
a'
b'
d'
e'
a
b(e)
c(d)
m' m'
c'
=55
a'
b'
c'
d'
e'
m' m1'
Locus of M
a
eb
c d
FTV

13. Page No. 13
Problem 27: A pentagonal lamina of the edges 25mm is resting on HP with one of its corners
Draw the top and front views of the lamina in this position. Determine the inclination of the
lamina with HP.
Solution:
Problem 28: A pentagonal lamina having edges 25mm is placed on one of its corner on HP such
that the perpendicular bisector of the edge passing through the corner on which the lamina rests is
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X
VP
HP
TV
FV
FFV
DTV
Y
a
b
c
d
e
a' b'(e') c'(d')
25
a
b
c
d
e
a'
b'(e')
c'(d')
a'
20
d
c
b
a
e
e'
b'
c'd'
X
VP
HP
FV
TV
DTV
Y
25
=55
a
b
c
d
e
m m1
Locus of M
FFV
a
b
c
d
e
m1 m
a' b'(e') c'(d')
a
b
c
d
e
a'
b'(e')
c'(d')
a'
b'
e'
d'c'

14. Problem 29: A pentagonal lamina of the sides 25mm is resting on one of its edges on HP with
one of its corner opposite to that edge touching VP. This edge is parallel to VP and the corner,
which touches VP, is at a height of 15mm above Hp. Draw the projection of the lamina and
determine the inclination of the lamina with HP and VP and the distance at which the parallel
edge lies from VP.
Solution:
Problem 30: A pentagonal lamina of sides 25mm is having a side both on HP and VP. The corner
opposite to the side on which it rests is 15mm above HP. Draw the top and front views of the lamina.
Solution:
Page No. 14
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
a
b
c
d
e
a'b'(e')c'(d')
25
FFV
a'
b'(e')
c'(d')
15
a
b
c
d
e
a
b
cd
e
36
a'
b'
c'd'
e'
DTV
X Y
VP
HP
TV
FV
a
b
c
d
e
a'b'(e')c'(d')
25
FFV
a'
b'(e')
c'(d')
15
a
b
c
d
e
a'
b'
c'd'
e'
DTV
a
b
cd
e

15. Problem 31: A pentagonal lamina of sides 25mm is having a side both on HP and VP. The surface
Solution:
Problem 32: A regular pentagonal lamina of 25mm side is resting on one of its corners on HP
and , draw the projection of the lamina.
Solution:
Page No. 15
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
a
b
c
d
e
a'b'(e')c'(d')
25
a
b
c
d
e
a'
b'(e')
c'(d')
FFV
DTV
a
e
dc
b
a'
e'
d'c'
b'
X
VP
HP
TV
FV
FFV
DTV
a
b
c
d
e
a' b'(e') c'(d')
a'
b'(e')
c'(d')
a
b
c
d
e
Y
25
a
b
cd
e
a'
b'
c'd'
e'

16. Problems on Hexagonal lamina
Problem 33: A regular pentagonal lamina of 25mm side is resting on one of its side on HP while
, draw the projection of the lamina.
Solution:
Problem 34: A hexagonal lamina of the sides 25mm rests on one of its sides on HP. The lamina
Solution:
Page No. 16
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
a
b
c
d
e
a'b'(e')c'(d')
25
a
b
c
d
e
a'
b'(e')
c'(d')
FFV
DTV
a'
e'
d'c'
b'
a
e
dc
b
X Y
VP
HP
TV
FV
FFV
DTV
25
a
b
c
d
e
f
a'(f') b'(e') c'(d') a'(f')
b'(e')
c'(d')
a
f
b
e
c
d
a
b
c
d
e
f
c'
b'
a'f'
e'
d'

17. Page No. 17
Problem 35: A hexagonal lamina of the sides 25mm rests on one of its sides on VP. The lamina
Solution:
Problem 36: A hexagonal lamina of the sides 25mm rests on one of its sides on VP. The side
opposite to the side on which it rests is 30mm infront of VP and the side on which it rests makes
plane.
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
DFV
25
a'
b'
c'
d'
e'
f'
a(f) b(e) c(d) a(f)
b(e)
c(d)
a'
f'
b'
e'
c'
d'
a'
f'
e'
d'
c'b'
dc
b
a f
e
FTV
X Y
VP
HP
TV
FV
DFV
25
a'
b'
c'
d'
e'
f'
a(f) b(e) c(d) a(f)
b(e)
c(d)
a'
f'
b'
e'
c'
d'
a'
f'
e'
d'
c'b'
dc
b
a f
e
FTV
30

18. Page No. 18
Problem 37: A regular hexagonal lamina of the sides 25mm is lying in such a way that one of its
sides on HP while the side opposite to the side on which it rests is on VP. If the lamina makes an
Solution:
Problem 38: Draw the top and front view of a hexagonal lamina of the sides 30mm having two
its edges parallel to both vertical and horizontal planes and one of its edges is 10mm from each of
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
FFV
DTV
25
a
b
c
d
e
f
a'(f') b'(e') c'(d') a'(f')
b'(e')
c'(d')
a
f
b
e
c
d
a
b
cd
e
f
c'
a'f'
e'
d'
b'
X Y
VP
HP
TV
FV
FFV
DTV
30
a
b
c
d
e
f
a'(f') b'(e') c'(d') a'(f')
b'(e')
c'(d')
a
f
b
e
c
d
a
b
cd
e
f
c'
a'f'
e'
d'
b'
10
1010

19. Page No. 19
Problem 40: A hexagonal lamina of the sides 25mm rests on one of its corners on HP. The
Solution:
Problem 39: A hexagonal lamina of the sides 25mm rests on one of its corners on HP. The
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
a
b c
d
ef
25
b'(f') c'(e')a' d'
a
b c
d
ef
a'
b'(f')
c'(e')
d'
a
b
c
d
e
f
d'
c'
b'
a'
f'
e'
FFV
DTV
X Y
VP
HP
TV
FV
a
b c
d
ef
25
b'(f') c'(e')a' d'
a1
b c
d
ef
a'
b'(f')
c'(e')
d'
a1
b
c
d
e
f
d'
c'
b'
a'
f'
e'
FFV
DTV
Locus of A
a

20. Page No. 20
Problem 41: A hexagonal lamina of the sides 25mm rests on one of its corners on HP. The
corner on which it rests is 35mm above Hp and the diagonal passing through the corner on which
surface with HP.
Solution:
Problem 42: A regular hexagonal lamina of the sides 25mm is lying in such a way that one of its
sides on HP while the corner opposite to the corner on which it rests is on VP. If the lamina
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
a
b c
d
ef
25
b'(f') c'(e')a' d'
a1
b c
d
ef
a'
b'(f')
c'(e')
d'
a1
b
c
d
e
f
d'
c'
b'
a'
f'
e'
FFV
DTV
Locus of A
a
35
X Y
VP
HP
TV
FV
a
b c
d
ef
25
b'(f') c'(e')a' d'
a
b c
d
ef
a'
b'(f')
c'(e')
d'
FFV
DTV
a
b
cd
e
f
d'
c'
b'f'
e'
a'

21. Page No. 21
Problem 43: A hexagonal lamina of the sides 30mm is resting on HP with one of its corners in
Solution:
Problem 44: A hexagonal lamina of the sides 30mm is resting on HP with one of its corners in
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
a'
X Y
VP
HP
TV
FV
b' c'
d'
e'f'
30
a f(b) e(c) d a
f(b)
e(c)
d
a'
b' c'
d'
e'f'
DFV
d'
a'
b'
c'
e'
f'
a
b
c
d
e
f
FFV
a'
X Y
VP
HP
TV
FV
b' c'
d'1
e'f'
30
a f(b) e(c) d a
f(b)
e(c)
d
a'
b' c'
d'
e'f'
DFV
d'1
a'
b'
c'
e'
f'
FFV
d'
Locus of D
a
b
c
d
e
f

22. Page No. 22
Problem 45: A hexagonal lamina of the sides 30mm is resting on HP with one of its corners
Solution:
Problem 46: A regular hexagonal lamina of the sides 30mm is lying in such a way that one of its
projections.
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
a'1
X Y
VP
HP
TV
FV
b' c'
d'
e'f'
30
a f(b) e(c) d
a'
b' c'
d'
e'f'
DFV
d'
a'
b'
c'
e'
f'
a
b
c
d
e
f
FTV
a
d
e(c)
f(b)
a'1
Locus of A
X Y
VP
HP
TV
FV
30
a1'
f1' e1'
d1'
b' c'b1' c1'
a1 d1
X1
Y1
RPP (LSV)
f1''(e1'')
a1''(d1'')
f''(e'')
a''(d'')
b''(d'')
b c
a
f e
d
a'
f' e'
d'

23. Problems on Circular lamina
Problem 48: Draw the projections of a circular plate of negligible thickness of 50mm diameter
Solution:
Problem 47: A regular hexagonal lamina of the sides 30mm is lying in such a way that one of its
sides touches both the reference planes. If the side opposite to the side on which it rests is 45mm
above HP, Draw its projections.
Solution:
Page No. 23
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
FFV
a
b
c
d
e
f
g
h
a' b'(h') c'(g') d'(f') e' a'
b'(h')
c'(g')
d'(f')
e'
a
b
c
d
e
f
g
h
DTV
a
b
c
d
e
f
g
h
e'
d'
c'
b'a'h'
g'
f'
X Y
VP
HP
TV
FV
30
a1'
f1' e1'
d1'
b' c'b1' c1'
a1 d1
X1
Y1
RPP (LSV)
f1''(e1'')
a1''(d1'')
f''(e'')
a''(d'')
b''(d'')
b c
a
f e
d
a'
f' e'
d'
45

24. Page No. 24
Problem 49: A circular lamina of 50mm diameter rests on HP such that one of its diameters is
Solution:
Problem 50: A circular lamina of 30mm diameter rests on VP such that one of its diameters is
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
a
b
c
d
e
f
g
h
a' b'(h') c'(g') d'(f') e'
a
b
c
d
f
g
h a
b
c
d
e e1
e1
f
gh
DTV
FFV
e'
f'
g'
h'a'
b'
c'
d'
Locus of E
X Y
VP
HP
TV
FV
FTV
DFV
a'
b'
c'
d'
e1'
f'
g'
h'
a h(b) g(c) f(d) e
g'
f'
e'
d'
c'
b'
a'
h'
a
h(b)
g(c)
f(d) e
Locus of E
h'
a'
b'
c'
d'
e' e1'
f'
g'
a
h
g
f e
d
cb

25. Page No. 25
Problem 51: A circular lamina of 50mm diameter is standing with one of its points on the rim on
passing through the point on which the lamina rests is parallel to VP. Draw its projections
Solution:
Problem 52: A circular lamina inclined to the VP appears in the front view as an ellipse of the
major axis 30mm and minor axis 15mm. The major axis is parallel to both HP and VP. One end
of the minor axis is in both the HP and VP. Draw its projections of the lamina and determine the
inclination of the lamina with the VP
Solution:
Prepared By
Raghavendra T. Anegundi
B.E.,M.Tech.,AMIE
X Y
VP
HP
TV
FV
FFV
a
b
c
d
e
f
g
h
a' b'(h') c'(g') d'(f') e' a'
b'(h')
c'(g')
d'(f')
e'
a
b
c
d
e
f
g
h
DTV
a
b
c
d
e
f
g
h
e'
a' h'
g'
f'd'
c'
b'
X Y
VP
HP
TV
FV
FTV
a'
d'
c'
b'
a d(b) c
a'
d'
c'
b'
15
30
a
d(b)
c
c'
d' b'
a'
a
b
c
d
DFV