The document provides information on the projection of plane figures: 1) It explains the basics of plane projection problems, including what is typically given (projections of the plane) and asked for (its position relative to reference planes). 2) Plane figures can have their surface parallel or inclined to the horizontal or vertical planes, and edges parallel or inclined to the other reference plane. The document demonstrates solving problems through 3 steps of initial positioning, surface inclination, and edge inclination. 3) Several example problems are worked through step-by-step to show determining the front, top, and side views of planes in different orientations, such as a pentagon inclined to the horizontal plane and a side to the vertical plane

2. BASICS OF PROJECTION OF PLANE
WHAT IS USUALLY ASKED IN THE PROBLEM ?
TO DRAW THEIR PROJECTIONS MEANS F.V, T.V. & S.V.
WHAT WILL BE GIVEN IN THE PROBLEM ?
 DESCRIPTION OF THE PLANE FIGURE.
 IT’S POSITION WITH HP AND VP.
 IN WHICH MANNER IT’S POSITION WITH HP & VP WILL BE DESCRIBED ?
INCLINATION OF IT’S SURFACE WITH ONE OF THE REFERENCE PLANES WILL BE GIVEN.
INCLINATION OF ONE OF IT’S EDGES WITH OTHER REFERENCE PLANE WILL BE GIVEN
(HENCE THIS WILL BE A CASE OF AN OBJECT INCLINED TO BOTH REFERENCE PLANES.)

3. PLANE/PLATE/LAMINA
• A PLANE IS A 2 DIMENSIONAL OBJECT HAVING LENGTH
AND BREADTH. VARIOUS SHAPES OF PLANE FIGURES ARE
SHOWN BELOW.

4. UNDERSTADING PROJECTION OF A PLANE
AND ITS TRACES
1) Any one of the planes given above is kept in first quadrant
with reference to VP and HP.
2) Trace of a plane is a line of intersection or meeting of the
plane surface with the reference plane.
3) There are six different positions in which a plane can be
placed with reference to its surface and reference planes (VP
& HP) and are discussed below.

5. CASE OF A RECTANGLE – OBSERVE AND NOTE ALL STEPS.
VP
HP
VP VP
a’ d’
b’ c’
HP
a
d
b c
a1’
d1’ c1’
b1’
HP
a1
d1
b1 c1
SURFACE PARALLEL TO HP
PICTORIAL PRESENTATION
SURFACE INCLINED TO HP
PICTORIAL PRESENTATION
ONE SMALL SIDE INCLINED TO VP
PICTORIAL PRESENTATION
ORTHOGRAPHIC
TV-True Shape
FV- Line // to xy
ORTHOGRAPHIC
FV- Inclined to XY
TV- Reduced Shape
ORTHOGRAPHIC
FV- Apparent Shape
TV-Previous Shape
A B C

6. PROCEDURE OF SOLVING THE
PROBLEM
 IN THREE STEPS EACH PROBLEM CAN BE SOLVED:( AS SHOWN IN
PREVIOUS ILLUSTRATION )
• STEP 1. ASSUME SUITABLE CONDITIONS & DRAW FV & TV OF
INITIAL POSITION.
• STEP 2. NOW CONSIDER SURFACE INCLINATION & DRAW 2ND FV &
TV.
• STEP 3. AFTER THIS , CONSIDER SIDE/EDGE INCLINATION AND
DRAW 3RD ( FINAL) FV & TV.

7. ASSUMPTIONS FOR INITIAL POSITION
(INITIAL POSITION MEANS ASSUMING SURFACE // TO HP OR VP)
• 1.IF IN PROBLEM SURFACE IS INCLINED TO HP – ASSUME IT // HP
• OR IF SURFACE IS INCLINED TO VP – ASSUME IT // TO VP
• 2. NOW IF SURFACE IS ASSUMED // TO HP- IT’S TV WILL SHOW TRUE SHAPE.
• AND IF SURFACE IS ASSUMED // TO VP – IT’S FV WILL SHOW TRUE SHAPE.
• 3. HENCE BEGIN WITH DRAWING TV OR FV AS TRUE SHAPE.
• 4. WHILE DRAWING THIS TRUE SHAPE –
• KEEP ONE SIDE/EDGE ( WHICH IS MAKING INCLINATION) PERPENDICULAR
TO XY LINE
• ( SIMILAR TO PAIR NO. A ON PREVIOUS PAGE ILLUSTRATION ).

8. A-1)Draw the projections of a regular pentagon of 40 mm side, having
its surface inclined at 45º to the H.P. and a side parallel to the H.P. and
inclined at an angle of 60º to the V.P.
a
b c
d
f e
a
’
b’
f’
c
’
e
’
d’ 45°
a1
f1 e1
d1
b1 c1
60°
a1
b1
c
1
d1
e1
f1
a1’
b1
’
c1’
d1
’
e1’
f1’
Plane parallel to HP
Plane inclined to HP
at 45°and ┴ to VP
Top view of the diagonal
making 60° with the VP.
Y
X
60°

9. STEPS
1) Draw the reference line XY.
2) Then draw the pentagon having side length equal to 30 mm and name it abcde
with suffix 1.It is top view of stage 1.
3) Then draw its projection on the HP as one of its side in the HP and name it
a’b’c’d’e’ with suffix 1.It is the front view of stage 1.
4) Then draw a line at an angle of 45 above the HP and shift all the distances of
previous front view and name it abcde with suffix 2.Hence it is the front view of
second stage.
5) Then taking the projection from front view and previous top view the top view of
second stage is been drawn and name it a’b’c’d’e’ with suffix 2.
6) Then draw a line at an angle of 60 in front of VP and shift all the distance of
previous top view and hence the final top view of the plane is ready and name it
abcde.
7) Now taking the projection of final top view and previous front view the final front
view is been drawn and name it a’b’c’d’e’.
In this way the projection of pentagonal plane is done.

10. B-1)A semicircular plate of 80mm diameter has its straight edge in the VP
and inclined at 45 to HP. The surface of the plate makes an angle of 30 with
the VP. Draw its projections.
Plane in the V.P. with
straight edge ┴ to H.P
1’
2’
3’
4’
5’
6’
7’
1
7
11’
21’
X Y
2
6
3
5
4 30º
31’
41’
51’
7 61’ 1’
45º 11
21
31
41
51
61
71
Ø 80
Plane inclined at 30º
to the V.P. and
straight edge in the
V.P.
St. edge in V.P. and
inclined at 45º to the
H.P.

11. STEPS
1) Draw the reference line XY.
2) Then draw the semicircle having radius equal to 40 mm and name it 1’2’3’4’5’6’7’ with
suffix 1.It is front view of stage 1.
3) Then draw its projection at 5 mm in front of the VP name it 1234567 with suffix 1.It is
the top view of stage 1.
4) Then draw a line at an angle of 30 in front of the VP and shift all the distances of
previous top view and name it 1234567 with suffix 2.Hence it is the top view of second
stage.
5) Then taking the projection from top view and previous front view the front view of
second stage is been drawn and name it 1’2’3’4’5’6’7’ with suffix 2.
6) Then draw a line at an angle of 45 above the HP and shift all the distance of previous
front view and hence the final front view of the plane is ready and name it
1’2’3’4’5’6’7’.
7) Now taking the projection of final front view and previous top view and hence the final
top view is been drawn and name it 1234567.
In this way the projection of semicircular plane is done.

12. B-2) Draw a rhombus of 100 mm and 70 mm long diagonals with longer
diagonal horizontal. The figure is the top view of a square having 100 mm
long diagonals. Draw its front view.
a’ b’d’ c’
c1
d1 b1
X Y
100
100
a
b
c
d
70
a’
b’
c’
d’
a1
b1
c1
d1
a1
d1 b1
c1
100
70
a1

13. STEPS
1) Draw the reference line XY.
2) Then draw the square having side length equal to 100 mm and name it abcd with
suffix 1.It is drawn in top view because one of its corner is in VP therefore its
apparent shape is drawn in VP. Hence it is the top view of stage 1 .
3) Then draw its projection on the HP as one of its corner is in the VP and name it abcd
with suffix 1.It is the front view of stage 1.
4) Then draw a rhombus that is the true shape having diagonal equal to 100 and 70 and
name it a’b’c’d’ with suffix 2.Hence it is the top view of second stage.
5) Then taking the projection from top view and shifting distances from previous front
view the front view of second stage is been drawn and name it a’b’c’d’ with suffix 2.
6) Then draw a rhombus that is the true shape having diagonal equal to 70 and 100 and
name it a’b’c’d’.Hence it is the final top view.
7) Now taking the projection of final top view and previous front view the final front
view is been drawn and name it abcd.
In this way the projection of rhombus plane is done.

14. C-2) A thin rectangular plate of sides 60 mm X 30 mm has its shorter side in
the V.P. and inclined at 30º to the H.P. Project its top view if its front view is a
square of 30 mm long sides.
b’ c’
b1’ c1’
X Y
a
b
30
a’
d’
60
c
d
a
b
c
d
a1’
d1’ a 30º 1 b1
c1 d1

15. STEPS
1) Draw the reference line XY.
2) Then draw the rectangle having dimension equal to 60 x 30 mm and name it
a’b’c’d’ with suffix 1.It is front view of stage 1.
3) Then draw its projection in the VP as its shorter side is in the VP and name it
abcd with suffix 1.It is the top view of stage 1.
4) Then draw a square of dimension 30 x 30 as its ront view is a square and name
it a’b’c’d’ with suffix 2.Hence it is the front view of second stage.
5) Then taking the projection from second stage front view draw the top view of
second stage and name it abcd with suffix 2.
6) Then draw a line at an angle of 30 above the HP and shift all the distance of
previous front view and hence the final front view of the plane is ready and
name it a’b’c’d’.
7) Now taking the projection of final front view and previous top view and hence
the final top view is been drawn and name it abcd.
In this way the projection of rectangular plane is done.

16. EXTRA-A 300 – 600 set square of longest side 100 mm long, is in VP and
300 inclined to HP while it’s surface is 450 inclined to VP. Draw it’s
projections
X Y
c1
300
450
a1’
b1’
c1’
a
c
a’
a
b1
b’
b
b a1
c
c’
Surface // to VP Surface inclined to Vp
side inclined to Hp
a1’
b1’
60º
30º