1. PROJECTION OF PLANES

2. Class A(1): Plane parallel to P.P. and hence
perpendicular to both H.P. & V.P.
Y
V.P.
a” V.P. P.P.
’ P.P a’,b’ a”
a’,b A . b”
d” b”
D YB c’,d’
d’ c” d” c”
c’,
C X Y
a,d a,d
H.P.
X
b,c
b,c
X H.P.

3. Class A(2): Plane parallel to V.P. and hence
perpendicular to both H.P. & P.P.
A, a’ B, d’ Y
V.P.
b’
a’
D, d’ F.V. C, c’ c’ Y B
X Y
d’ A
C
c
b, .P.
X D H
a,d
a, d b, c
T.V. X

4. Class A(3): Plane parallel to H.P. and hence
perpendicular to both V.P. & P.P.
Y
.P.
V d’
c’,
D a’,b’
a’ ,b’ c’,d’
C F.V.
A
Y X Y
B
d
a d
a c .
P
X H.
b
b c
X T.V.

5. Class B(1): Plane perpendicular to V.P. and inclined
to H.P. by  & also inclined to P.P.
Y
V .P.
b’, c’
b’, c’
.
a’, d’

F.V.
B
Y C

X Y
a’, d’ A b
a b D  .P.
X a c H
d
d c
T.V. =  X

6. Exercise 01:
A regular hexagonal plate
ABCDEF, 30mm side, is resting
on H.P. on one of the
sides/edges with surface of the
plate making 45º with H.P. and
perpendicular to V.P. Draw the
projections of the plate.

7. Data Given:
(1) Hexa. Plate Size = 30mm V.P .
(2)  = 45°
d’,e’
E
c’,f’ Y
D
F
f e
a’,b’
d ’e’ A,a
C d
H. P.
’f’ F,f E,e
’ c c
a’b B ,b
X A,a D,d
C,c
B,b

8. Data Given:
(1) Hexa. Plate Size = 30mm
d1’,e1’
(2)  = 45°
c1’,f1’
a’,b’ c’,f’ d’,e’ a1’,b1’ 
X f f1 Y
a e a1 e1
30
b d b1
c d1
Scale: 1:1
c

9. Class B (2): Plane perpendicular to H.P. and inclined
to V.P. by Φ & also inclined to P.P.
Y
P.
.
a’ b’ V.
b’
a’
d’ c’ 
F.V. Ac’ B
Y
X Y d’
.
a, d

D C
X a, d 
c .P.
b, H
T.V. b, c
= X

10. Exercise 02:
A square plate PQRS, edge
25mm size, is in space with one
of its corners on V.P. Surface of
the plate makes 60º with V.P.
and it is perpendicular to H.P.
Draw its projections.

11. Data Given:
V.P.
- Square Plate Size=25mm s’
- Φ=60º r’ S
S ,s’ P,p’
R,r’
R
q’ Y
Φ Q
P ’ p
p q,s
,q’ r r
Q H.P.
q,s
p
X
X

12. Data Given:
(1) Square Plate Size=25mm s’
S s1’
(2) Φ=60º
P r’ p ’
p’ 1 r1’
R
q’ Q q1’
X Y
p q,s r p1
Φ
q1,s1
r

13. Class B (3): Plane perpendicular to P.P. and inclined
to H.P. by  & to V.P. by Φ
Y P.
V.
b’ P.P
a”,b” .
a’ B 
A Y

 c”,
d’ d”
C
X a 
cH.P.
D
Z d X

14. Exercise 03:
A rectangular plate PQRS 30mm X
60mm size, is in space with
shorter edge parallel to H.P. and
20mm above it. Plate PQRS is
perpendicular to V.P. and inclined
to H.P. by such an angle so that
its plan becomes square. Draw
the projections.

15. Data Given: c1’d1’
- Size of rectangle=30mmX60mm
-Distance of plane from H.P.=20mm
.
(plane is parallel to H.P.)
T.L
- Size of Plan=square of
30mm X 30mm θ
a’,b’ c’,d’ a1’,b1’
20
X Y
A,a D,d a1 d1
30
b1 c1
B C,c
,b 60 30

16. Exercise 04:
A regular pentagonal plate of
30mm sides, has one of its corners
on H.P. The plane of the pentagon
is inclined at 45º to the H.P. The
side of the pentagon, which is
opposite to the corner, which is on
H.P. is inclined at 30º to the V.P.
Draw the projections of the plate.

17. Data Given - Size of Pentagonal Plate =30mm
-  = 45°
-  = 30°
c1’,d1’ d2’ c2’
L.
e2’
T.
b1’,e1’
b 2’
a’ b’,e’ c’,d a1’ θ
X e a2’ Y
’ e1 Φ
d d2
30
d1
e2 c2
a a1
c c1
a2 b2
b b1
Scale = 1:1

18. Exercise 05:
Draw the projections of a circle of
75mm diameter resting on the
H.P. on a point A of the
circumference. Plane is inclined
to the H.P. such that the plan of it
is an ellipse of minor axis 30mm.
The plan of the diameter,
thorough the point A, is making
an angle of 30º with the V.P.
Measure the angle of the plane
with the H.P.

19. Data Given:
(1) Circle Dia.=75mm
(2) =30°
e1’ e2’
(3) Minor axis plan f2’
d1’,f1’ d2’
length=30mm
g 2’
.
c2’
T.L
c1’,g1
75 b1’,h1 ’ h2’
a’ b’,h c’,g’ d’,f’ e’ ’a1’ θ a2’ b2’
X ’ g g1 g2  Y
f2
h f h1 f1 h2 e 2
e a1 e1 a2
a
d2
b1 d1 b2 c
b d 2
c c1
30
Scale:1:

20. Exercise 06:
A regular hexagonal plate
40mm side is resting on one of
its edges on H.P. The plane
makes an angle of 30º to H.P.
and its longest diagonal makes
an angle of 45 º with V.P. Draw
its projections.

21. Data given :-
(1) Regular hexagonal plate size = 40mm
(2) Θ =30º
(3) = = 45º Scale = 1:1
d1’e1’ e2’ d2’
L
T. f2’
a’b’ c’f’ d’e’ a 1’b 1’ θ c1’f1’ a2’ c2’
X f f1 b2 ’ e Y
 f 2
2
a e a1 e1
d2
40
a2
b d b1 d1
c2
c c1 b2

22. Exercise 07:
A square plate of side 50mm
is held on a corner on H.P.
with a diagonal horizontal
and inclined at 40º to V.P. The
plate is seen as a rhombus in
plan with one of its diagonals
measuring 40mm. Draw its
projections and determine the
angle it makes with H.P.

23. Data Given:
(1)Plate =50mm sq.
(2)Plate Diagonal =parallel to H.P. & at 40° ( ) to V.P.
(3)Plate is seen as rhombus with one diagonal=40mm
c1’ c2’
L
d2’
R=
L b2’
b1’d1’
a’ b’d’ c’ a1’ 
X a2’ Y
d d1 =
d2
50
c2
T.S. c
a a1 c1
square
a2 b2
b1
b 40

24. Exercise 08:
A regular pentagon ABCDE, of
25mm sides, has its side AB in
the V.P. and inclined at an
angle of 45º to the H.P. The
corner A is 20mm above H.P.
and the corner D is 25mm in
front of V.P. Draw the
projections of the plane and
find its inclination with the V.P.

25. Data Given:-
(1) Regular pentagonal plate size=25mm
(2)  =45° -:Answer:-
(3) A= 20 mm above XY line
 = 31°
(4) D= 25 mm below XY line
e’ e1’ d2’ c2’
a’ a1’
d’
25
d1’ e2’ b2 ’
b’ b1’ a2’
c’ c1’
 a2
02
X a1,b1  b2 Y
a,b c,e d
c2
25
c1,e1 e2
Scale=1:1 Locus of d d1 d2

26. Exercise 09:
A 30º- 60º set square has its
shortest side 40mm long and is in
the H.P. The top view of the set
square is an isosceles triangle
and the hypotenuse of the set
square is inclined at an angle of
45º with the V.P. Draw the
projections of the set square and
find its inclination with the H.P.

27. Data:- Answer:-
(1) T.L.(AB)=40mm (1) θ = 55º
(2) Φ=45º Locus of c’
c1’ c2’
.L.
R=T
a’,b’ c’ a1’,b1’ θ b2 ’ a2’
X Y
a a1 a2
T.L Φβ
60º .
P.
40
40
T.
L.
L.
P.L
30º c1
b c b1 40 b2
.
c2
Scale:-1:1
Locus of c

28. Exercise 10:
ABCD is a rhombus of diagonals
AC=120mm and BD=60mm. Its
corner A is in the H.P. and the
Plane is inclined to the H.P.
such that the plan appears to be
a square. The plan of diagonal
AC makes an angle of 30º to the
V.P. Draw the projections of
the plane and find its inclination
with H.P.

29. Data:-
(1) Size of rhombus = 120 mm X 60mm
(2) =30º
c1’ c2’
Answer:-
(1) θ = 60º
.
T.L
d2 ’
b2 ’
b1’d1’
a’ b’,d’ c’ a1’  a2’
X Y
d d1
d2
c1
60
a c a1 c2
120 b 60 b1 a2 30º
b2
Scale:-1:1

30. Exercise 11:
A regular hexagonal plate 40mm
side is resting on one of its
corners in H.P. The diagonal
through that corner is inclined
at 30º to H.P. and
(a)the plan of that diagonal is
inclined to V.P. by 30º and
(b)diagonal is inclined at 30º.
Draw its projections.

31. Data Given:-
(1) Hexagonal plate size=40mm
(2) =30°
(3) =30° [for case (a)]
(4) =30° [for case (b)]
. d1’ d2’ d2’
L e 2’ e2’
T. c ’e ’ c 2’ c 2’
b1’f1’ 1 1
f2’
X a’ b’f’ c’e’ d’ a1’  f 2’ b2’ b’ Y
f f1 a2’ e  a2’ e2 2 d
e e1 2 d2 1 
f2 f2
d2
a d a1 d1 β
Φ c2
a2 c2 a2
b b2
40 c b1 c1 b2
Locus of d
Scale=1:1