An Autonomous Institution
Affiliated to VTU, Belagavi,
Approved by AICTE, New Delhi,
Recognised by UGC with 2(f) & 12 ( B)
Accredited by NBA & NAAC
ENGINEERING GRAPHICS
MVJ20EGR15/25
Prepared by: Prof. Chandrasekhar G L
Prof. Niranjan Hugar
Assistant Professor,
Department of Mechanical Engineering
1
PROJECTION OF PLANE
SURFACES
2
What is Projection of Planes
A plane is a two dimensional object having length and breadth only .Its
thickness is always neglected .Various shapes of plane figures are
considered such as square, rectangle, circle, pentagon, hexagon, etc.
3
Projection of Planes
Meaning of Trace of a Plane
• It is defined as the extension of a given plane shape to the
reference plane (HP or VP) to which it is perpendicular or
inclined.
• The plane meets the HP or VP as a line.
• This line is called trace of a plane.
Horizontal Trace(HT) &Vertical Trace (VT) a plane.
• The line in which the plane shape meets the HP is called
HT.
• The line in which the plane shape meets the VP is
called as VT.
4
Orientation of Planes in Space
The following position of Planes in space
• Planes Parallel to VP and Perpendicular to HP
• Planes Perpendicular to VP and Parallel to HP
• Planes Parallel to
both VP and HP or
both Perpendicular VP and HP
• Planes Perpendicular to VP and Inclined to HP
• Planes Inclined to VP and Perpendicular to HP
• Planes Inclined to both VP and HP
Notations of object in Planes
Following notations should be followed while
naming different views projections of planes.
Object
Point
It’s top view
a , b, c ,…
It’s front view
a’ , b’, c’,…
It’s side view
a’’, b’’, c’’,…
6
Position in Projection of Planes
1.A plane perpendicular to HP and parallel to VP
7
Position in Projection of Planes
2.A plane perpendicular to VP and parallel to HP
8
Position in Projection of Planes
3.A plane perpendicular to both VP and HP
9
Position in Projection of Planes
4. A plane inclined to HP and perpendicular VP
10
Position in Projection of Planes
5. A plane inclined to VP and perpendicular HP
11
Position in Projection of Planes
6. A plane inclined to both VP and HP
12
Position in Projection of Planes
6. A plane inclined to both VP and HP
13
Position in Projection of Planes
A plane resting on one of its base side on HP
A plane resting on one of its base side on VP
14
Position in Projection of Planes
A plane resting on one of its corner on HP
A plane resting on one of its corner on VP
15
1. An Equilateral triangular lamina of 25mm side lies with one of its edges
on HP such that the surface of the lamina is inclined to HP at 60°. The
edge on which it rests is inclined to VP at 60 °. Draw the projections.
b'
c'(a')
VP
X
HP
b'
a
c'(a')
a
b
25
c
60°
b
c
b'
a'
60°
c'
a
Y
b
c
16
2. An Equilateral triangular lamina of 25mm side lies with one of its sides on
HP. The lamina makes 45° with HP and one of its medians is inclined at
40° to VP. Draw its projections.
VP
X
HP
c'(a')
b'
a
25 d1
c
c'(a')
b'
b'
45°
a'
40° β
a
b
d2
c
c'
Y
b
c
b
a
d2 d1
locus of D
17
3. A triangular lamina of 25mm 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° to HP and 45° to VP. Draw its projections.
25
a'
b'
d 1'
b'
b'
a'
c'
c'
X
VP
HP
d1'
d2'
d2'
a'
c'
30° α
a
b(c)
a
Y
a
45°
b(c)
locus of D
b
c
18
4. A triangular lamina of 25mm sides rests on one of its corners on HP such
that the surface of the lamina makes an angle of 60° with HP. If the side
opposite to the corner on which the lamina rests makes an angle of 30°
with VP. Draw its projections.
c'(b')
a'
VP
X
HP
c'(b')
a'
b'
60°
30°
b
b
c'
a'
Y
b
c
a
a
a
25
c
c
19
5. A triangular lamina of 25mm sides rests 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 makes an angle of 30° with VP. Draw its projections.
Also determine the inclination of the lamina with the reference plane.
c'(b')
a'
VP
X
HP
c'(b')
a'
b
a
15
θ
30°
b
c
c'
a'
Y
b
c
a
25
b'
a
c
Ans: Lamina Inclination = 44°
20
6. A 30°-60° setsquare of 60mm longest side is so kept such that the longest
side is in HP, making an angle of 30° with VP. The setsquare itself is
inclined at 45° to HP. Draw the projections of the setsquare.
b'
VP
X
HP
c'(a')
b'
c'(a')
b'
45°
a'
30°
a
a
a
30°
60
60°
c
c'
Y
b
c
b
b
c
21
7. An isosceles triangular plate of negligible thickness has base 25mm long
& altitude 35mm. It is so placed on HP such that in the front view it is
seen as an equilateral triangle of 25mm sides with the side that is parallel
to VP is inclined at 45 ° to HP. Draw its top and front views. Also
determine the inclination of the plate with the reference plane.
35
a'
VP
X
HP
25
25
a'
b'
c'
a(c)
b
b'
c'
b'
c'
a(c)
a'
a
ɸ
b
45°
c
Y
b
Ans: Lamina Inclination = 52°
22
8.
A square lamina of 40mm side rests on one of its sides on HP. The
lamina makes 30° to HP and the side on which it rests makes 45° to VP.
Draw its projections.
c'(b')
VP
X
HP
d'(a')
a
c'(b')
b
d‘(a')
a
a'
d'
30°
45°
b
d
c
d
c
Y
a
b
d
40
b'
c'
c
23
9.
A square plate of 30mm sides rests on HP such that one of the diagonals
is inclined at 30° to HP and 45° to VP. Draw its projections.
c'
c'
d' (b')
VP a'
X
HP
d'(b')
c'
a'
b
b'
30°
d'
a'
b
c
b
c
a
a
β
c
d
a
40
d
Y
45°
Locus of A
d
24
10. A square lamina ABCD of 40mm side rests on corner C such that the
diagonal AC appears to be at 45° to VP. The two sides BC and CD
containing the corner C make equal inclinations with HP. The surface of
the lamina makes 30° with HP. Draw its top and front views.
a'
a'
d'(b')
VP a'
X
HP
d'(b')
c'
30°
b
c'
b
c
a
a
b'
c' 45°
b
d
c
c
a
40
d'
d
d
25
11. The top view of a square lamina of side 30mm is a rectangle of sides
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?
c'(b')
c'
b'
X1
c"(b")
42°
VP d'(a')
X
HP
a
c'(b') d‘(a')
b
θ
a
b
d'
a'
d"(a")
d
a
45°
c
b
48° RPP
Y
30
d
c
d
20
c
Y1
Ans: Lamina Inclination : HP = 48° & VP = 42°
26
12. A rectangular lamina of sides 20mm x 30mm 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°. The edge on which it rests is
inclined at 30° to VP. Draw the projections of the lamina.
c'(b')
VP d'(a')
X
HP
a
c'(b')
b
d'(a')
a
c'
45°
d'
a'
a
b
d
30
d
20
c
d
b'
c
30°
Y
b
c
27
13. A rectangular lamina of 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 edge on which the lamina rests
being parallel to both HP & VP. Draw its projections and find its
inclinations to HP & VP.
X1
c'(b')
c'
c"(b")
b'
35°
VP d'(a')
X
HP
a
θ
c'(b')
d'(a')
b
a
b
c
d
c
d'
a'
d"(a")
d
a
45°
c
b
55° RPP
Y
20
d
35
20
Ans: Lamina Inclination : HP = 55° & VP = 35°
Y1
28
14. A rectangular lamina of 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 edge on which the lamina rests
is inclined at 30° to VP. Draw its projections & find its inclinations to HP.
c'(b')
VP d'(a')
X
HP
a
c'(b')
b
c'
θ
d'(a')
a
a'
d'
30°
b
20
b'
Y
a
d
d
35
c
d
b
c
20
c
Ans: Lamina Inclination = 55° to HP
29
15. A rectangular lamina of sides 20mm x 25mm has an edge in HP and
adjoining edge in VP. It is tilted such that the front view appears as a
rectangle of 20mm x 15mm. The edge which is in VP is 30mm from RPP.
Draw the top, front and left profile views in this position and find its
inclinations with the corresponding principal planes.
25
b'
X1
15
c'
b'
c'
b"
c"
d'
c(d)
a'
b(a)
d'
a"
d"
(LSV)
20
X
VP
HP
a'
b(a)
ɸ
RPP
Y
45°
c(d)
30
Ans: Lamina Inclination = 53° to VP
Y1
30
16. The front view of a rectangular lamina of sides 30mm x 20mm is a
square of 20mm sides. Draw the projections and determine the
inclinations of the lamina with HP and VP.
30
a'
20
b'
a'
20
b'
d'
VP
X
HP
X1
b'
a(d)
c'
b(c)
c'
d'
a(d)
b"(c")
c'
ɸ
48°
a'
a
d'
d
42° RPP
a" (d")
Y
45°
b(c)
Ans: Lamina Inclination : HP = 42° & VP = 48°
b
c
Y1
31
17. 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 appear
perpendicular to both HP and VP. Draw the projections and find the
inclinations of the mirror with the wall.
40
a'
30
b'
a'
30
b'
d'
VP
X
HP
X1
b'
a(d)
c'
b(c)
c'
d'
a(d)
b"(c")
c'
ɸ
41°
a'
a
d'
d
49°
a"(d")
RPP
Y
45°
b(c)
Ans: Lamina Inclination : HP = 49° & VP = 41°
b
c
Y1
32
18. A rectangular plate of negligible thickness of size 35mm x 20mm has one
of its shorter edges in VP with that edge inclined at 40° to HP. Draw the
top view if its front view is a square of side 20mm.
35
a'
20
a'
b'
b'
b'
20
d'
VP
X
HP
c'
c'
d'
a'
a
a(d)
b(c)
a(d)
c'
d'
d 40°
Y
ɸ
b(c)
b
c
Ans: Lamina Inclination : VP = 55°
33
19. A pentagonal lamina of edges 25mm is resting on HP with one of its
sides such that the surface makes an angle of 60° with HP. The edge on
which it rests is inclined at 45° to VP. Draw its projections.
c'
c'
d'
d'(b')
VP
X
HP
e'(a')
a
d'(b')
e'(a')
c'
b
a
60°
e
a'
a
c
Y
45°
b
e
c
e
d
e'
b
c
25
b'
d
d
34
20. A pentagonal lamina of edges 25mm is resting on HP with one of its corners such
that the plane surface makes an angle of 60° 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 this corner make an angle of 45° with VP and
nearer to the observer, draw the top and front views of the lamina in this
position.
d'(c')
d'
c'
e'(b')
X
VP
HP
a'
e'(b')
b
d'(c')
c
c
e
Y
45°
b
a
a
d
b'
a'
b
a
25
e'
60°
a'
c
d
e
e
d
35
21. A pentagonal lamina of edges 25mm is resting on HP with one of its
corners such that the edge opposite to this corner is 20mm above HP &
makes an angle of 45° with VP. Draw the top & front views of the plane
lamina in this position. Determine the inclination of the lamina with HP.
d'(c')
c'
e'(b')
VP
X
HP
a'
e'(b')
b
d'(c')
θ
a'
b'
e'
a'
b
c
c
Y
45°
c
b
a
a
25
20
d'
d
e
d
d
e
a
e
Ans: Lamina Inclination : HP = 31°
36
22. A pentagonal lamina of sides 25mm 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 15mm above HP. Draw the
projections of the lamina and determine the inclinations of the lamina with
HP and VP and the distance at which the parallel edge lies VP.
X1
c'
d'(b')
VP e'(a')
X
HP
a
d'(b')
e'(a')
c'
b
a
θ
15
b'
d'
a'
b
D
c
25
c'
b"(d")
θ
RPP
a"(e")
Y
d 45°
c
e
d
φ
e'
b
a
e
c
c"
d
Ans: Lamina Inclination : HP = 23° & VP = 67°
Distance of parallel edge from VP = 35.43
e
Y1
37
23. A pentagonal lamina having edges 25mm is placed on one of its corners
on HP such that the perpendicular bisector of the edge passing through
the corner on which the lamina rests is inclined at 30° to HP and 45° to
VP. Draw the top and front views of the lamina.
d'(c')
d'
c'
e'(b')
VP
X
HP
a'
e'(b')
b
a
25
d'(c')
e'
30°
c
d
a
c
a
b'
Y
45° a'
b
m1
e
a'
b
m
d
e
e
c Locus of M
d
m m1
38
24. 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.
c'
d'(b')
VP
X
HP
e'(a')
a
d'(b')
e'(a')
c'
b
a
θ
15
d'
b'
e'
a'
e
b
c
25
c'
c
Y
a
b
d
c
e
e
d
d
Ans: Lamina Inclination : HP = 23°
39
25. A pentagonal lamina of sides 25mm is having a side both on HP and VP.
The surface of the lamina is inclined at an angle of 60° with HP. Draw the
top and front views of the lamina.
c'
c'
d'
d'(b')
VP
X
HP
e'(a')
a
d'(b')
e'(a')
c'
b
a
60°
25
e
e'
a'
e
b
c
b'
b
d
c
Y
a
c
e
d
d
40
26. A regular pentagonal lamina of 25mm side is resting on one of its
corners on HP while the side opposite to this corner touches VP. If the
lamina makes an angle of 60° with HP and 30° with VP, draw the
projections of the lamina.
d'(c')
c'
d'
e'(b')
VP
X
HP
a'
e'(b')
b
d'(c')
a'
c
b
c
c
a
a
25
b'
60°
e
d
a'
b
e'
Y
d
e
a
d
e
41
27. A pentagonal lamina having edges 25mm is placed on one of its corners
on HP such that the surface makes an angle 30° with HP and
perpendicular bisector of the edge passing through the corner on which
the lamina rests appears to be inclined at 30° to VP. Draw the top and
front views of the lamina.
d'(c')
d'
e'(b')
VP
X
HP
a'
e'(b')
b
d'(c')
30°
c
c
a
e
30° a'
b
a
25
a'
e'
d
c'
b'
Y
b
a
c
m
d
e
e
m
d
42
28. A regular pentagonal lamina of 25mm 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 60° with HP and 30° with VP, draw the projections of the
lamina.
c'
c'
d'(b')
VP
X
HP
e'(a')
a
d'(b')
e'(a')
c'
b
a
60°
e
b
b
c
25
d'
b'
c
a'
a
c
e'
d
Y
e
e
d
d
43
29. A pentagonal lamina of the edges 25mm is resting on VP with one of its
sides such that the surface makes an angle of 60° with VP. The edge on
which it rests is inclined at 45° to HP. Draw its projections.
b'
b'
a'
c'
c'
25
c'
e'
e'
VP
X
HP
b'
a'
d'
d'
a(e)
b(d)
c
a(e)
a'
45° e'
b
b(d)
c
Y
e
a
60°
d'
d
c
44
30. A pentagonal lamina having edges 25mm is placed on one of its corners
on VP such that the surface makes an angle 30° with VP and
perpendicular bisector of the edge passing through the corner on which
the lamina rests appears to be inclined 30° to HP. Draw the top and
front views of the lamina.
b'
25
b'
e'
a
b(e)
m'
d'
a
30°
a
30°
b(e)
d'
a'
d'
e'
c(d)
c'
b'
m'
a'
a'
VP
X
HP
c'
c'
e'
e
b
c(d)
Y
c
d
45
31. A pentagonal lamina having edges 25mm is placed on one of its corners
on VP such that the surface makes an angle 30° with VP and
perpendicular bisector of the edge passing through the corner on which
the lamina rests is inclined at 45° to HP. Draw the top and front views of
the lamina.
b'
25
c'
c'
m1'
a'
VP
X
HP
c'
b'
e'
a
b(e)
a'
b'
m'
d'
a'
d'
a
b(e)
e'
45° α
e'
c(d)
m' m1'
Locus of M
d'
a
30°
e
b
c(d)
Y
c
d
46
32. A hexagonal lamina of 30mm sides rests on HP with one its corners
touching VP and the surface inclined at 45° to it. One of its edges is
inclined to HP at 30°. Draw the front and top views of the lamina in its
final position.
b'
30
c'
b'
d'
a'
c'
a'
c'
d'
d'
b'
e'
e1'
Locus of E
VP
X
HP
f'
a b(f)
e'
c(e)
d
a
e'
f'
b(f)
45°
a'
b
α 30°
f'
f
a
e
c
c(e)
d
Y
d
47
33. Draw the top and front views of a hexagonal lamina of 30mm sides
having two of its edges parallel to both VP & HP and one of its edges is
10mm from each of the planes of projection. The surface of the lamina
is inclined at an angle of 60° to the HP.
d'(c')
d'
e'(b')
f'(a')
VP
X
HP
e'(b')
d'(c')
f'(a')
a
60°
10
b
c
b'
e'
10
b
a
c
30
f'
a'
f
a
d
e
f
Y
b
e
d
f
c'
c
d
e
48
34. A regular hexagonal lamina of sides 30mm is lying in such a way that
one of its edges touches both the reference planes. If the lamina makes
60° with HP, draw the projections of the lamina.
d'(c')
d'
e'(b')
VP
X
HP
f'(a')
e'(b')
d'(c')
f'(a')
b
a
60°
f'
f
a
d
c
e
f
a'
a
e
30
f
b'
e'
b
c
c'
Y
b
d
c
d
e
49
35. A regular hexagonal lamina of sides 30mm is lying in such a way that
one of its sides touches both the reference planes. If the sides opposite
to the side on which its rests is 45mm above HP, draw the projections of
the lamina.
d'(c')
d'
e'(b')
VP
X
HP
f'(a')
e'(b')
d'(c')
f'
f
b
c
a
d
c
e
f
a'
a
e
30
f
b'
e'
f'(a')
b
a
45
c'
Y
b
d
c
d
e
50
36. A regular hexagonal lamina of sides 25mm is lying in such a way that
one of its sides is on HP while the side opposite to the side on which it
rests is on VP. If the lamina makes 60° to HP, Draw the projections of the
lamina.
d'(c')
c'
e'(b')
VP
X
HP
f'(a')
e'(b')
d'(c')
f'(a')
b
a
b'
60°
a
d
c
e
f
f'
d
b
25
f
e'
a'
c
b
c
d'
Y
e
a
f
d
e
51
37. A regular hexagonal lamina of side 25mm is lying in such a way that one
of its corners is on HP while the corner opposite to the corner on which
it rests is on VP. If the lamina makes 60° to HP, Draw the projections of
the lamina.
d'
d'
e'(c')
VP
X
HP
a' f'(b')
b
e'(c') d'
c
f
e
60°
b
d
a
25
f'(b')
a'
e'
c'
c
b'
a'
c
d
d
f
e
Y
f
b
a
f'
a
e
52
38. A hexagonal lamina of sides 30mm is resting on HP with one of its
corners in VP and its surface inclined at an angle of 30° with VP. The
diagonal passing through that corner which is in VP is inclined at 45° to
HP. Draw the projections of the lamina.
Make a note that some portion
of lamina must touch XY line as
lamina rests on HP
b'
30
c'
VP
HP
c'
c'
d' d1'
Locus of D
d'
a'
X
b'
f'
a b(f)
e'
c(e)
d
a'
a
d'
f'
b(f)
b'
a'
e'
30°
e'
b
45°
a
α
e
c
c(e)
d
Y
f'
f
d
53
39. A hexagonal lamina of sides 30mm is resting on HP with one of its
corners in VP and its surface inclined at an angle of 30° with VP. The
diagonal passing through that corner which is in VP appears to be
inclined at 45° to HP. Draw the projections of the lamina.
b'
30
c'
d'
a'
VP
X
HP
b'
f'
a b(f)
e'
c(e)
d
c'
c'
d'
a'
a
d'
f'
b(f)
b'
e'
e'
30°
45°
a'
b
a
c
c(e)
d
Y
f'
f
e
d
54
40. A hexagonal lamina of sides 25mm rests on one of its sides on HP. The
lamina makes 45° to HP and the side on which it rests makes 30° to VP.
Draw its projections.
c'
d'(c')
e'(b')
VP
X
HP
f'(a')
e'(b')
d'(c')
f'(a')
a
45°
c
a
e'
b'
a'
30°
b
b
d'
b
c
d
a
25
f
d
e
d
f
Y
f'
c
f
e
e
55
41. A hexagonal lamina of sides 25mm rests on one of its corners on HP. The
lamina makes 45° to HP and the diagonal passing through the corner on
which it rests is inclined at 30° to VP. Draw its projections.
d'
d'
e'(c')
VP
X
HP
a' f'(b')
b
e'(c') d'
a
25
f
f'(b')
a'
c
e
f'
45°
b
d
e'
c'
b'
30° a'
a
c
Y
b
c
a
d
f
e
f
e
d
d1
Locus of D
56
42. A hexagonal lamina of sides 25mm rests on one of its corners on HP.
The lamina makes 45° to HP and the diagonal passing through the
corner on which it rests appears to be inclined at 30° to VP. Draw its
projections.
d'
d'
e'
e'(c')
VP
X
HP
a' f'(b')
b
e'(c') d'
f'(b')
a'
c
f'
45°
b
c'
b'
b
30° a'
c
Y
c
a
d
a
a
d
d
f
25
f
e
f
e
e
57
43. A hexagonal lamina of sides 25mm rests on one of its sides on VP. The
lamina makes 45° to VP and the side on which it rests makes 45° to HP.
Draw its projections.
b'
b'
a'
c'
a'
c'
c'
b'
25
f'
X
VP
HP
d'
b(e)
a'
e'
e'
a(f)
d'
f'
d'
c(d)
a(f)
45° f'
b(e)
e
b
c(d)
Y
f
a
45°
e'
c
d
58
44. A hexagonal lamina of sides 25mm rests on one of its sides on VP. The
side opposite to the side on which it rests is 30mm in front of VP & the
side on which it rests makes 45° to HP. Draw its projections. Also
determine the inclination of the lamina with the reference plane.
b'
b'
a'
c'
a'
c'
c'
b'
25
f'
X
VP
HP
d'
e'
e'
a(f)
b(e)
a'
d'
f'
d'
c(d)
a(f)
45° f'
30
b(e)
c(d)
Ans: Lamina Inclination to VP = 44°
Y
f
a
Ø
e'
e
b
c
d
59
45. A hexagonal lamina of sides 25mm rests on one of its corners on HP. The
corner opposite to the corner on which it rests is 35mm above HP & the
diagonal passing through the corner on which it rests is inclined at 30° to
VP. Draw its projections. Find the inclination of the surface with HP.
d'
d'
e'(c')
VP
X
HP
a' f'(b')
b
e'(c') d'
a
25
f
35
f'(b')
a'
c
θ
b
d
e'
f'
c'
b'
30° a'
a
c
Y
b
c
a
e
d
f
e
f
e
d
d1
Locus of D
Ans: Lamina Inclination to HP = 45°
60
46. Draw the projections of a circular plate of negligible thickness of 50mm
diameter resting on HP on a point A on the circumference, with its plane
inclined at 45° to HP and the top view of the diameter passing through
the resting point makes 60° with HP.
f'(d')
e'
VP
X
HP
b
Ø50
c
d
b
e
a
h
g
h'(b')
a'
f
a
c
g
g'
b'
45°
h'
a'
d
f
d
Y
60°
e
c
e
c
h
f'
c'
g'(c')
a' h'(b') g'(c') f'(d') e'
e'
d'
f
b
a
h
g
61
47. A circular lamina of 50mm diameter is standing with one of its points on
the rim on HP and the lamina inclined at 45° to HP. The diameter at right
angles to the diameter which is passing through the point on which the
lamina rests is parallel to VP. Draw its projections.
f'(d')
e'
g'(c')
VP
X
HP
a' h'(b') g'(c') f'(d') e'
b
Ø50
c
d
b
e
a
h
g
h'(b')
a'
f
a
d'
g'
45°
c
g
c'
h'
h
d
a'
a
b'
Y
b
g
e
c
h
f'
e'
c
f
e
d
f
62
48. A circular lamina of 50mm diameter rests on HP such that one of its
diameters is inclined at 30° to VP and 45° to HP. Draw its front and top
views in this position.
f'(d')
e'
VP
X
HP
a' h'(b') g'(c') f'(d') e'
b
Ø50
c
d
b
e
a
h
g
f
a
c
g
c'
h'
45°
30° β
d
f
b'
a'
Y
b
a
e
c
h
d'
g'
g'(c')
h'(b')
a'
e'
f'
c
d
h
g
e
Locus of E
f
63
49. A circular lamina inclined to VP appears in the front view as an ellipse of
major axis 30mm and minor axis 15mm. The major axis is parallel to
both VP and HP. One end of the minor axis is in both VP and HP. Draw
the projections of the lamina and determine the inclination of the
lamina with the VP.
b'
Ø30
X
VP
HP
15
c'
c'
d'
e'
a'
h'
a (h)
b
g'
(g)
c
f'
(f)
d
d'
b'
e
a'
e'
h' g' f'
a
b(h) Ø
c(g)
d(f)
Ans: Lamina Inclination : VP = 60°
e
d'
e'
f'
g'
c'
b'
b
a'
a
h'
h
c
Y
g
d
e
f
64
50. A circular lamina of 30mm diameter rests on VP such that one of its
diameters is inclined at 30° to VP and 45° to HP. Draw its top and front
views in this position.
d'
b'
Ø30
VP
X
HP
c'
d'
b'
e'
a'
h'
a (h)
b
g'
(g)
c
f'
(f)
d
e
c'
c'
d'
a'
g'
a
b(h)
30°
c(g)
d(f)
f'
g'
a'
45° α
b a
c
e
Locus of E
f'
b'
e'
h'
e'
d
h'
h
e
g
Y
f
65
Questions
An equilateral triangular lamina of 25mm side lies with one of its edges on HP
such that the surface of the lamina is inclined to HP at 600. The edge on which it
rests is inclined to VP at 600. Draw the projections.
A triangular lamina of 25mm sides rests on one of its on VP such that the median
passing through the corner on which it rests is inclined at 300 to HP and 450 to
VP. Draw its projections.
A 300-600 setsquare of 60 mm longest side is so kept such that the longest side is
in HP, making an angle of 300 with VP. The setsquare itself is inclined at 450 to
HP. Draw the projections of the setsquare.
A square plate of 30mm sides rests on HP such that one of its diagonals is
inclined at 300 to HP and 450 to VP. Draw its projections.
A rectangular lamina of 35mm*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 is inclined at 300 to VP. Draw
the projections and find its inclination to HP.
RBT LEVEL
L2
L2
L2
L2
L2
66
Questions
RBT LEVEL
A pentagonal lamina of edges 25mm is resting on HP with one of its sides such
that the surface makes an angle of 600 with HP. The edge on which it rests is
inclined at 450 to VP. Draw its projections.
L2
A pentagonal lamina of sides 25mm is resting on one of its edges on HP with the
corner opposite to that edge touching VP. The edge is parallel to VP and the
corner, which touches VP is at a height of 15mm above HP. Draw the projections
of the lamina and determine the inclinations of the lamina with HP.
L2
A pentagonal lamina having edges 25mm is placed on one of its corners on HP
such that the perpendicular bisector of the edge passing through the corner on
which the lamina rests is inclined at 300 to HP and 450 to VP. Draw the top and
front views of the lamina.
A hexagonal lamina of 30mm sides rests on HP with one of its edges and the
surface is inclined at 450 to it. Draw the projections of the lamina when the
resting edge is inclined at 300 to VP.
A circular lamina of 50mm diameter rests on HP such that one of its diameters is
inclined at 300 to VP and 450 to HP. Draw the projections of the lamina.
L2
L2
L2
67
NPTEL Link
https://youtu.be/dCWjBvZBpjM
By Prof. Nihar Rajan Patra
Department of Civil Engineering
IIT Kanpur
•
68