Projections of Planes
1. (1) An equilateral triangular lamina of 25 mm sides lies with one of its edges on HP such that the
surface of the lamina is inclined to HP at 60 deg. The edge on which it rests is inclined to VP at 60
deg. Draw its projections.
Solution:
a'
VP a'
b'(c')
b'(c')
HP
c
c
c
a
b'
c'
a
Y
60
°
X
60
°
a'
a
25
b
b
b
2 (4) A Triangular plane figure of sides 25 mm is resting on HP with one of its corners, such that the
surface of the lamina makes an angle of 60 deg. with HP. If the side opposite to the corner on which
the lamina rests makes an angle of 30 deg. with VP. Draw the top and front views in this position.
Solution:
c'
c'
c'
Y
a
c
b
c
b
25
a
c
HP
Girish Hanumaiah
b'
30 °
(a') b'
VP
a'
a
X
60
°
(a') b'
b
Page 21
Projections of Planes
3. (6) A 30 - 60 deg. set square of 60 mm longest side is so kept such that the longest side is in HP
making an angle of 30 deg. with VP. The set square itself is inclined at 45 deg. to HP. Draw the
projections of the set square.
Solution:
a'
45°
VP a'
b' (c')
(c')
b'
c'
b' Y
HP
30 °
X
a'
c
c
c
30°
b
Solution:
a
a
a
°
60
b
b
4. (8) A square lamina of 40 mm side rests on one of its sides on HP. The lamina makes 30 deg. to
HP and the side on which it rests makes 45 deg. to VP. Draw its projections.
X
(d')
a'
(c')
b'
30 °
VP
b'(c')
HP
c
d
d
a'
c'
c
c
d
a
b
a
b
b'
Y
45°
d'
(d') a'
b
a
40
Girish Hanumaiah
Page 22
Projections of Planes
5. (12) A rectangular lamina of sides 20 mm X 30 mm rests on HP on one of its longer edges. The
lamina is tilted about the edge on which it rests till its plane surface is inclined to HP at 45 deg. The
edge on which it rests is inclined at 30 deg. to VP. Draw its projections of the lamina.
Solution:
(d') a'
b'(c')
c'
HP
c
d
d
c
c
b'
d
30
Y
30°
X
(c')
b'
45°
(d')
a'
VP
a'
d'
b
a
a
20
b
a
b
6. (19) A pentagonal lamina of edges 25 mm is resting on HP with one of its sides such that the
surface makes an angle of 60 deg. with HP. The edge on which it rests is inclined at 45 deg. to VP.
Draw its projections.
Solution:
a'
a'
b' (e')
a'
c' (d')
e'
b'
c' (d')
d'
HP
d
d
d
a
c
a
a
b
c
c
25
b
Girish Hanumaiah
Y
e
e
e
c'
45°
VP
X
60
°
b' (e')
b
Page 23
Projections of Planes
7. (20) Pentagonal lamina of edges 25 mm is resting on HP with one of its corners such that the plane
surface makes an angle of 60 deg. with HP. The two of the edges containing the corner on which the
lamina rests make equal inclinations with HP. When the edge opposite to the corner makes an angle of
45 deg. with VP and nearer to the observer. Draw the top and front views of the plane lamina in this
position.
a' (e')
e'
a'
Solution:
VP
X
a' (e')
60
°
b' (d')
b' (d')
d'
b'
c'
c'
c'
Y
d
45 °
HP
d
d
c
e
25
e
e
c
c
a
b
a
a
b
Edge opposite to the corner nearer
b
to the observer
9. (40) A hexagonal lamina of sides 25 mm rests on one of its sides on HP. The lamina makes 45
deg. to HP and side on which it rests makes 30 deg. to VP. Draw its projections.
Solution:
a' (f')
f'
45 °
b' (e')
b' (e')
e'
b'
(d')
c'
(d') c'
f'
HP
e
c'
Y
30°
X
a' (f')
VP
a'
e
d
e
f
d f
d
25
c
a
c
c
a
f
b
a
b
Girish Hanumaiah
b
Page 25
Projections of Planes
10. (2) An equilateral triangular lamina of 25 mm sides lies on one of its sides on HP. The lamina
makes 45 deg. with HP and one of its medians is inclined at 40 deg. to VP. Draw the projections.
Solution:
a'
45°
VP
(c') b'
a'
X
a'
b' (c')
c'
b'
Y
40°
HP
a
c
c
c
b
a
a
25
b
b
β = 65.36
11. (9) A square plate of 30 mm sides rests on HP such that one of the diagonals is inclined at 30
deg. to HP and 45 deg. to VP. Draw its projections.
Solution:
a'
a'
b'(d')
b' (d')
c'
c'
d
a
d
c
d'
c'
c'
a
β
45°
VP a'
X
HP
b'
d
c b
a
c
30
b
Girish Hanumaiah
b
β = 53.10
Page 26
Projections of Planes
12. (23) A pentagonal lamina having edges 25 mm is placed on one of its corners on HP such that
the perpendicular bisector of the edge passing through the corners on which the lamina rests is
inclined at 30 deg. to HP and 45 deg. to VP. Draw the top and front views of the lamina.
Solution:
VP
a' (e')
b' (d')
c'
a'
b' (d')
e'
b'
d'
c'
c'
HP
Y
β
c
d
X
30°
a' (e')
d
d
e
25
b
e
e
c
a
c
a
a
b
b
β = 51.6
51 .63
.63
13. (41) A hexagonal lamina of sides 25 mm rests on one of its corners on HP. The lamina makes
45 deg. to HP and the diagonal passing through the corner on which it rests is inclined at 30 deg. to
VP. Draw its projections.
Solution:
a'
a'
f'
VP
(e')
c' d'
b'
(e')
c'
e'
d'
e
HP
e
f
f
a
c'
d'
β
d
e
f
d
d a
30°
X
a'
(f')
b'
45 °
(f') b'
c
a
b
b
Girish Hanumaiah
25
c
b
c
β = 44.9
44 .99
.99
Page 27
Projections of Planes
14. (48) A circular lamina of 50 mm diameter rests on HP such that one of its diameter is inclined at
30 deg. to VP and 45 deg. to HP. Draw its top and front views in this position.
a'
Solution:
a'
b' (h')
h'
b'
(g')
g'
VP
HP
g
d' (f')
e'
g
h
f
h
f
f'
d'
30 °
X
45°
c'
g
β
a
h
f
b
e a
a
e
e
c
d
b
b
d
d
c
c
β = 44.9
44 .99
.9 9
50
15. (50) A circular lamina of 30 mm diameter rests on VP such that one of its diameter is inclined at
30 deg. to VP and 45 deg. to HP. Draw its top and front views in this position.
Solution:
50
g'
f'
d'
g'
f'
a'
a'
e'
h'
f'
e'
a
h (b)
c'
g(c)
b'
d'
β
b'
d'
b'
a'
c'
e'
h'
h'
g'
c'
f(d) e
e
e
f
f(d)
c
g(c)
a
h (b)
d
g
h
a
b
β = 54.7
54 .74
.7 4
Girish Hanumaiah
Page 28
Projections of Planes
16. (3) A triangular lamina of 25 mm sides rests on one of its corners on VP such that the median
passing through the corner on which it rests is inclined at 30 deg. to HP and 45 deg. to VP. Draw its
projections.
Solution:
a'
a'
a'
c'
b'
c'
α
VP
a (b)
HP
c
45°
X
b'
b'
30°
25
c'
Y
c
c
a
a (b)
b
α = 45
17. (31) A pentagonal lamina having edges 25 mm is placed on one of its corners on VP such that
the surface makes an angle 30 deg. with VP and perpendicular bisector of the edge passing through
the corner on which the lamina rests is inclined at 45 deg. to HP. Draw the top and front views of the
lamina.
d'
d'
e'
c'
c'
b'
b'
HP
a (e)
d (b)
c
a (e)
c
45°
VP
30°
X
b'
e'
a'
a'
α
a'
25
c'
d'
e'
Y
c
d
b
d (b)
e
a
α = 54.7
4. 7 3
Girish Hanumaiah
Page 29
Projections of Planes
18. (38) A hexagonal lamina of sides 30 mm is resting on HP with one of its corners in VP and its
surface inclined at an angle of 30 deg. with VP. The diagonal passing through that corner which is in
VP is inclined at an angle 45 deg. to HP. Draw the projections of the lamina.
c'
Solution:
d'
30
c'
b'
c'
e'
b'
b'
a'
d'
a'
f'
d'
a'
VP
f'
a
b
(f)
e'
30°
HP
f'
e'
c d
(e)
45°
X
α
d
d
c
(e) c
b
(f) b
Y
e
f
a
a
α = 54.7
4. 72
19. (10) A square lamina ABCD of 40 mm side rests on corner C such that diagonal AC appears to
be at 45 deg. to VP. The two sides BC and CD containing that corner C make equal inclination with
HP. The surface of the lamina makes 30 deg. with HP. Draw its top and front views.
Solution:
a'
VP
X
b' (d')
a'
30 °
a'
c'
b' (d')
d'
b'
c'
c'
Y
HP
d
d
a
c
45 °
d
c
c
a
a
b
40
b
Girish Hanumaiah
b
Page 30
Projections of Planes
20. (27) A pentagonal lamina having edges 25 mm is placed on one of its corners on HP such that
the surface makes an angle 30 deg. with HP and perpendicular bisector of the edge passing through
the corner on which tha lamina rests appears to be inclined at 30 deg. to VP. Draw the top and front
views of the lamina.
Solution:
X
a' (e')
b' (d')
b' (d')
30°
VP
e'
a' (e')
c'
a'
b'
c'
d'
c'
d
d
d
c
e
25
e
Y
30°
HP
e
c
c
b
a
a
a
b
b
21. (42) A hexagonal lamina of sides 25 mm rests on one of its corners onHP. The lamina makes
45 deg. to HP and the diagonal passing through the corner on which it rests appears to be inclined
at 30 deg. to VP. Draw its projections.
Solution:
a'
a'
b'
VP
(e')
c' d'
f'
(e')
c'
e'
d'
HP
30 °
X
a'
(f')
b'
45 °
(f') b'
e
f
f
a
d
Y
f
e
e
a
d
a
c'
d'
d
b
c
b
Girish Hanumaiah
25
c
b
c
Page 31
Projections of Planes
22 (46) Draw the projections of a circular plate of negligible thickness of 50 mm diameter resting on
HP on a point A on the circumference, with its plane inclined at 45 deg. to HP and the top view of the
diameter passing through the resting point makes 60 deg. with VP.
a'
a'
h'
b' (h')
(h')
b'
c' (g')
d' (f') e'
d' (f')
e'
f'
g
h
f
a
e
a
b
d
b
a
e
h
d
f
g
h
d'
e'
°
60
g
c'
g'
f
VP a'
X
HP
45 °
c' (g')
b'
e
Solution:
d
b
c
c
50
23. (30) A pentagonal lamina having edges 25 mm is placed on one of itscorners on VP such that
the surface makes an angle of 30 deg. with VP and perpendicular bisector of the edge passing
through the corner on which the lamina rests appears to be inclined at 30 deg. to HP. Draw the top
and front views of the lamina.
Solution:
d'
d'
e'
e'
c'
25
e'
c'
c'
a'
a'
b'
30°
b'
b'
a'
VP
HP
a (e)
d (b)
c
30°
X
d'
a (e)
Girish Hanumaiah
c
d
c
Y
b
d (b)
e
a
Page 32
Projections of Planes
24. (38) A hexagonal lamina of sides 30 mm is resting on HP with one of its corners in VP and its
surface inclined at an angle of 30 deg. with VP. The diagonal passing through that corner which is in
VP is inclined at an angle 40 deg. to HP. Draw the projections of the lamina.
Solution:
c'
30
c'
b'
d'
a'
VP
a
d'
f'
e'
c(e) d
e'
a'
e'
f'
c
d
30°
HP
f'
b (f)
c'
a'
d'
b'
40°
X
b'
(e) c
b
(f) b
d
Y
e
f
a
a
25. (5) A triangular plane lamina of sides 25 mm is resting on HP with one of its corners touching it,
such that the side opposite to the corner on which it rests is 15 mm above HP and make an angle of
30 deg. with VP. Draw the top and front views in this position. Also determine the inclination of the
lamina to the reference plane.
Solution:
a'
b'
15
(a') b'
(a') b'
VP
c'
θ
c'
HP
a
c'
Y
30°
X
b
b
b
c
c
a
25
c
a
ANSWER
θ = 43.86
Girish Hanumaiah
Page 33
Projections of Planes
26. (21) A pentagonal lamina of edges 25 mm is resting on HP with one of its corner such that the
edge opposite to this corner is 20 mm above HP & makes an angle of 45 deg. with VP. Draw the top
and front views of the plane lamina in this position. Determine the inclination of the lamina with HP.
Solution:
e'
20
a' (e')
a' (e')
b' (d')
c'
b' (d')
HP
b'
d'
c'
c'
Y
d
45°
X
VP
θ
a'
c
d
d
e
e
e
25
b
c
c
a
a
a
b
b
ANSWER
θ = 31.32°
27. (45) A hexagonal lamina of sides 25 mm rests on one of its corners on HP. The corner opposite
to the corner on which it rests is 35 mm above HP and the diagonal passing through the corner on
which it rests is inclined at 30 deg. to VP. Draw its projections. Find the inclination of the surface with
HP.
a'
a'
Solution:
(f') b'
f'
b'
θ
(e')
c'
c'
d'
HP
30 °
X
a'
(e')
c' d'
45°
VP
35
(f')
b'
e
f
f
a
d
d
a
f
a
e
e'
Y
d'
e
b
d
c
b
25
c
b
c
ANSWER
θ = 43.43°
Girish Hanumaiah
β= 44.99°
Page 35
Projections of Planes
28. (44) A hexagonal lamina of sides 25 mm rests on one of its sides on VP. The side opposite to the
side on which it rests is 30 mm infront of VP and the side on which it rests makes 45 deg. to HP. Draw
its projections. Also determine the inclination of the lamina with the reference plane.
Solution:
b'
b'
a'
c'
c'
b'
c'
25
a'
d'
a'
d'
f'
e'
e'
VP
HP
a
(f)
b
(e)
c
(d)
c
c(d)
φ
Y
d
b
30
X
e'
f'
45 °
d'
f'
e
(e) b
a
a (f)
ANSWER
f
φ = 43.86°
29. (14) A rectangular lamina of 35 mm X 20 mm rests on HP 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 is inclined at 30 deg. to VP. Draw its projections and find its inclination to HP.
(d') a'
X
VP
a' (d')
c'
θ
b'(c')
(c') b'
d'
HP
b'
a'
c
d
c
d
Y
30°
Solution:
b
c
20
d
a
a
35
Girish Hanumaiah
b
b
a
20
ANSWER
θ= 55.15°
Page 36
Projections of Planes
30. (13) A rectangular lamina of 35 X 20 mm 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.
X1
Solution:
d'
a' (d')
RPP
a'
d' (a")
φ
X
θ
(c') b'
VP a' (d')
(c') b' c'
b'
c
b
d
a
c"
(b")
θ
Y
HP
d
c
c
20
d
a
35
b
a
20
b
Y1
ANSWERS: Inclination of Lamina to HP (θ) = 55.15°
Inclination of Lamina to VP (φ) = 34.85°
31. (18) A rectangular plate of negligible thickness of size 35 X 20 mm has one of its shorter edges
in VP with that edge inclined at 40 deg. to HP. Draw the top view if its front view is a square of side
20 mm.
Solution:
a'
b'
20
35
b'
a'
b'
c'
d'
X
c'
c'
d'
d'
40°
20
a'
VP
HP a (d)
(c) b
φ
a (d)
b
(c) b
c
a
d
Y
Girish Hanumaiah
Y
ANSWER
φ = 43.86°
Page 37
Projections of Planes
32. (16) The front view of a rectangular lamina of sides 30 mm X 20 mm isa square if 20 mm sides.
Draw the projections and determine the inclination of the surface of the lamina with HP and VP.
Solution:
X1
20
b'
a'
20
a" (b")
b'
30
a'
HP
d'
a
(d)
c'
b
(c)
(c") d"
c'
d'
d
θ
RPP
c
Y
45°
X
VP
φ
a
b
Y1
θ = 41.81°
φ = 48.19°
33. (11) The top view of a square lamina of side 30 mm is a rectangle of sides 30 mm X 20 mm with
a 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 lamina with HP and VP.
Solution:
X1
a' (d')
d'
RPP
d' (a")
a'
φ
X
θ
(c') b'
VP a' (d')
(c') b' c'
HP
d
d
c
c
θ
Y
b
30
c
c"
(b")
b'
d
a
30
Girish Hanumaiah
b
a
20
b
a
Y1
ANSWERS
θ = 48.19°
φ = 41.81°
Page 38
Projections of Planes
34. (22) A pentagonal lamina of sides 25 mm is resting on one of its edges on HP with the corner
opposite to that edge touching VP. This edge is parallel to VP and the corner, which touches VP is at
a height of 15 mm above HP. Draw the projections 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:
X1
a'
a'
a'
b' (e')
15
VP
(d') c'
(d')
e'
c'
c'
b" (e")
φ
d'
(d")c"
θ
a
HP
b
e
e
d
e
Y
L=?
X
a"
b'
b' (e')
d
a
c
d
a
25
Y1
c
c
b
ANSWERS
b
θ = 22.95°
φ = 67.05°
35 (24) A pentagonal lamina of sides 25 mm is having a side both on HP and VP. The corner opposite
to the side on which it rests is 15 mm above HP. Draw the top and front views of the lamina.
Solution:
a'
X
15
a'
VP
(e')
b'
(d') c'
a'
b' (e')
e'
d'
d
(d') c'
HP
e
e
b'
c'
c
e
b
d
d
a
Y
a
a
25
c
b
Girish Hanumaiah
c
b
Page 39
Projections of Planes
36. (35) A regular hexagonal lamina of side 30 mm 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 45 mm above HP. Draw
the projections of the lamina.
Solution:
(f') a'
b' (e')
45
X
(e')
b'
(f')
a'
VP
a'
f'
(d') c'
e'
b'
c'
d'
d
(d')
HP
c'
c
Y
e
e
b
e
a
f
d
f
c
a
d
30
f
c
a
b
b
37. (25) A pentagonal lamina of sides 25 mm is having a side on both HP and VP. The surface of the
lamina is inclined at an angle of 60 deg. with HP. Draw the top and front views of the lamina.
Solution:
a'
a'
X
VP
a'
b' (e')
60
°
b'(e')
c'(d')
e'
(d')
c'
b'
d'
d
HP
c'
c
e
e
e
a
a
25
c
b
Girish Hanumaiah
b
d
d
a
Y
c
b
Page 40
Projections of Planes
38. (26) A regular pentagonal lamina of 25 mm side is resting on one of its corner on HP while the
side opposite to this corner touches VP. If the lamina makes an angle of 30 deg. with HP and 60 deg.
with VP. Draw the projections of the lamina.
X1
Solution:
Solution:
X
a' (e')
b' (d')
c'
b'
b' (d')
30°
VP
c'
e
a
HP
d
b" (d")
c"
Y
d
b
e
e
°
60
d'
c'
d
a" (e")
e'
30 °
a'
a' (e')
c
25
c
c
a
a
b
b
Y
1
39. (28) A regular pentagonal lamina of 25 mm side is resting on one of its sides on HP while the corner
opposite to this side touches VP. If the lamina makes an angle of 60 deg. with HP and 30 deg. with VP.
Draw the projections of the lamina.
Solution:
X1
a'
a'
b'(e')
a"
e'
b'
b" (e")
(d') c'
HP
c'
d'
a
b
e
60
°
(d')
c'
60
(e')
b'
45°
X
VP a'
°
30°
e
RPP
c"
Y
(d")
e
d
d
a
c
d
a
25
c
b
c
b
Y1
Girish Hanumaiah
Page 41
Projections of Planes
40. (34) A regular hexagonal lamina of 30 mm sides lying in such a way that one of its sides touches
both the reference planes. If the lamina makes 60 deg. with HP. Draw the projections of the lamina.
Solution:
a'
a' (f')
VP
X
(f')
a'
(e')
b'
b'
e'
60
°
(e') b'
f'
(d')
c'
c'
c
(d') c'
HP
d'
d
Y
e
b
e
e
d
f
a
c
a
f
d
30
f
a
c
b
b
41. (36) A regular hexagonal lamina of sides 25 mm is lying in such a way that one of its sides on HP
while the side opposite to the side on which it rests on VP. If the lamina makes 60 deg. to HP. Draw
the projections of the lamina.
a' (f')
Solution:
a'
VP
X
(f')
a'
(e')
b'
b'
e'
60
°
(e') b'
f'
(d')
c'
c'
a
(d') c'
HP
d'
f
e
b
e
e
d
f
a
c
a
c
d
d
30
f
Y
b
Girish Hanumaiah
c
b
Page 42
Projections of Planes
41. (37) A regular hexagonal lamina of side 25 mm is lying in such a way that one of its corners on
HP while the corner opposite to the corner on which it rests on VP. If the lamina makes 60 deg. to
HP. Draw the projections of the lamina.
Solution:
a'
a'
(f') b'
X
(f')
b'
VP a'
(e')
c'
(e') c'
d'
f'
b'
e'
c'
d'
d'
e
HP
a
f
c
25
Y
b
d
e
d
a
d
b
c
f
e
f
a
c
b
43. (33) Draw the top and front views of a hexagonal lamina of 30 mm sides having two of its edges
parallel to both HP and VP and one of its edges 10 mm from each of the planes of projection. The
surface of the lamina is inclined at an angle of 60 deg. to the HP.
a'
a' (f')
Solution:
(e') b'
(d')
c'
c'
(d') c'
VP
d'
Y
HP
10
X
e'
10
(e')
b'
b'
60
°
(f')
a'
f'
e
e
d
f
a
c
a
d
e
b
d
a
f
30
f
c
b
Girish Hanumaiah
c
b
Page 43
Projections of Planes
44. (47)
A circular lamina of 50 mm diameter is standing with one of its points on the rim on HP and
the lamina inclined at 45 deg. to HP. The diameter at right angle to the diameter which is passing
through the point on which the lamina rests is parallel to VP. Draw its projections.
Solution:
a'
a'
h'
b' (h')
g'
c' (g')
(h')
b'
c' (g')
d' (f') e'
g
c'
d' (f')
e'
45 °
VP a'
X
HP
b'
f'
e'
g
h
e
h
f
d'
f
f
d
c
g
a
e
e
a
b
h
b
d
a
d
b
c
c
50
45. (7) An isosceles triangular plate of negligible thickness has base 25 mm long and altitude 35 mm
it is placed on HP such that in the front view is seen as an equilateral triangle of 25 mm sides with the
side that is parallel to VP is inclined at 45 deg. to HP. Draw its top and front views. Also determine the
inclination of the plate with the reference plane.
Solution:
35
a'
X
VP
25
b'
b'
a'
b'
a'
c'
c'
c'
Y
HP
a
b(c)
φ
a
Girish Hanumaiah
c
b(c)
a
b
φ = 51.79°
Page 44
Projections of Planes
46. (15) A rectangular lamina of sides 20 mm X 25 mm has an edge in HP and adjoining edge in VP,
is tilted such that the front view apears as a rectangle of 20 mm X 15 mm. The edge which is in VP is
30 mm from the right profile plane.
a) Draw the top view, front view and the left profile view in this position.
b) Find its inclinations with the corresponding principal planes.
Solution:
X1
30
25
RPP
15
b'
a'
b'
d'
c'
d'
c'
b (c)
b"
a"
VP c"
d"
20
a'
X
(d) a
Y
HP
45°
φ
b(c)
(d) a
Y1
φ = 53.13°
47. (17) A mirror 30 mm X 40 mm is inclined to the wall such that its front view is a square of 30 mm
side. The longer side of the mirror appear perpendicular to both HP and VP. Find the inclination of the
mirror with the wall.
Solution:
30
40
b'
a'
b'
d'
c'
b'
c'
a'
d'
30
a'
d'
X
c'
VP
HP
a
(d)
b
(c)
φ
(d) a
b(c)
a
d
b
Y
c
φ = 41.41°
Girish Hanumaiah
Page 45
Projections of Planes
48. (32). A hexagonal lamina of 30 mm sides rests on HP with one of its corners touching VP and the
surface inclined at 45 deg. to it. One of its edges inclined to HP at 30 deg. Draw the top and front views
of the lamina in its final position.
Solution:
30
c'
b'
c'
c'
b'
b'
d'
X
f'
d'
e'
e'
f'
45°
VP
HP
a'
a
c
(e)
b
(f)
30°
a'
d'
d
e'
a'
α
f'
d
(e) c
Y
f
b
d
e
c
(f) b
a
a
ANSWER
α = 32.31°
49. (49) A circular lamina inclined to the VP appears in the front view as an ellipse of major axis 30mm
& minor axis 15 mm. The major axis is parallel to both HP and VP. One end of the minor axis is in both
the HP and VP. Draw the projections of the lamina and determine the inclination of the lamina with the
VP.
Solution:
15
g'
g'
f'
h'
e'
a'
30
h'
f'
a'
b'
e'
a'
h'
g'
c'
d'
b'
X
HP
a h
(b)
g
(c)
d'
e
φ f(d)
g(c)
d
c'
c'
VP
d'
b'
f e
(d)
h (b)
a
f'
e'
e
Y
f
g
c
b
a
h
ANSWER
φ = 60.00°
Girish Hanumaiah
Page 46