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Projections of planes
1
1 An isosceles triangle ABC with base AB = 42 mm and height 58 mm rests with AB on HP and 600 to VP with point A 18 mm in front
of VP. Complete the projections of triangular plate, its surface inclined at 450 to HP.
Initial Step: Assume triangular plane is simply kept
on H.P. True shape will be observed in T.V. Edge view
a’b’ on HP; draw side ab of triangle abc perpendicular
to VP. Point a should be 18 mm in front of VP.
Draw edge view in FV.
Inclination with HP: Surface i.e.
edge view makes 450 with HP.
Reproduce FV making an angle 450
with HP. Draw vertical projectors
from FV and horizontal projector
from TV of initial position and get
TV.
Inclination with VP: Resting edge ab
makes an angle 600 with VP. Reproduce TV
from second position as shown in third step.
Draw vertical projector from TV and
horizontal projectors from FV of second
position and get final FV.
M S Shinge
Projections of planes
2
2 A regular hexagonal plate 50 mm side is resting on one of its corners in HP the diagonal through that corner is inclined at 400 to HP
and TV of that diagonal inclined to VP by 300. Draw its projections.
Initial position: Assume hexagonal plate is
laying on HP. True shape of plate will be
observed in TV. Corner is in HP; draw
hexagon as shown in TV. Accordingly draw
FV which is edge view of plate.
Inclination with HP: Reproduce
FV such that its diagonal ‘ad’
makes an angle 400 with HP.
Draw TV by drawing projectors.
Draw accordingly TV.
Inclination with VP: Reproduce TV such that ‘ad’
makes 300 with VP. Draw final FV.
M S Shinge
Projections of planes
3
3 A 300-600 set square has its shortest side 50 mm long and is in the HP. The TV of the setsquare is an isosceles triangle and the
hypotenuse of the set square is inclined at an angle of 400 with the VP. Draw the projections of the setsquare and find its inclination
with the HP.
Initial position: 1) Plane is resting in HP: -
True shape will appear in HP. Draw first TV
2) Resting on shortest edge :-
Draw edge ab vertical at left side.
3) Draw FV
Inclination with HP:- 1) The TV
of the setsquare is an isosceles
triangle. Draw isosceles triangle in
TV (ab=ac=50) using horizontal
projectors from initial position.
2) Draw vertical projectors to draw
FV.
3) Draw FV. (a’-b’-c’)in first step
= a’-b’-c’)in second step
Inclination with VP:- 1) the hypotenuse of the set
square is inclined at an angle of 400 with the VP. As true
angle of hypotenuse is given and we have its apparent
length, find apparent angle. Apparent angle is 650. Draw
line making an angle 650 with VP. Mark hypotenuse cb
and reproduce TV from second position. 2) Draw final
FV by using vertical and horizontal projectors.
M S Shinge
Projections of planes
4
4 A thin plate has a rhombus shape with its diagonals of 50 mm and 80 mm length. It rests on one of its corners on HP. with a shorter
diagonal to be perpendicular to VP and parallel to HP. The longer diagonal is inclined to HP in such a way that the top view of plate
looks likes a square. Draw FV, TV and LHSV and measure the inclination with HP.
Initial position: A thin plate has a rhombus shape rests
on one of its corners on HP, with a shorter diagonal to
be perpendicular to VP and parallel to HP.
1. Draw TV(diagonal ‘bd’ perpendicular to VP)
2. Draw FV
Inclination with HP: The longer diagonal is inclined
to HP in such a way that the top view of plate looks
likes a square.
1. Draw TV such that it is square. (bd=ac)
2. Draw FV using vertical and horizontal projectors.
𝜃 is inclination with HP.
Draw SV
M S Shinge
Projections of planes
5
5 Triangle ‘abc’ carries ab=55, bc=65 and ca=50mm. ‘ab’ lies in HRP and point ‘a’ is 15 mm in front of FRP. Distance between
projectors of ‘a’ and ‘b’ is 45 mm. Complete the projections if point c is 45 mm above HRP.
1. Side ‘ab’ of triangle ‘abc’ lies in HRP. Point
‘a’ is 15 mm in front of FRP. Assume triangle
is simply kept in HP. True shape will appear in
TV. Draw TV such that side ab is vertical and
point ‘a’ is 15 mm in front of FRP.
2. Draw FV.
1. Point c is 45 mm above HRP.
Reproduce FV such that c is 45 mm
above HP.
2. Draw TV using vertical and
horizontal projectors.
𝜃 is inclination with HP.
1. Distance between projectors of a and b is 45
mm.
Draw two projectors at distance 45 mm from
each other. Reproduce TV.
2. Draw FV by using vertical and horizontal
projectors.
M S Shinge
Projections of planes
6
6 A rectangular plate 40×80 mm rests on one of its smaller side on FRP. Its front view appears like a square with all sides 40 mm.
Complete the projections of the plate if one of its diagonals is parallel to HP. Determine the inclination of the plate with FRP.
1. A rectangular plate rests on one of its smaller
side on FRP. Assume plate is kept in FRP and
draw true shape of plate in FV. Draw one smaller
side vertical.
2. Draw TV. by using vertical and horizontal
1. FV appears like a square. Draw square
in FV,
2. Reproduce TV by using vertical
projectors.
3. 𝜃 is inclination with FRP.
One diagonal is parallel to HP.
1. Reproduce FV such that diagonal bd is
parallel to HP.
2. Draw TV by using vertical and
horizontal projectors.
M S Shinge
Projections of planes
7
projectors.
7 A regular pentagon ‘abcde’ with all sides 40 mm has side ab in FRP and at 300 to HRP with corner ‘a’ 40 mm above HRP. Complete
its projection if‘d’ is 25 mm in front of FRP. Determine its inclination with FRP.
1. As one side of pentagon is in FRP, assume it
is simply kept in FRP. True shape will appear
in FRP i.e. FV. Draw pentagon in FRP with
one side vertical.(F.V.) Corner ‘a’ should be
40 mm above H.R.P. in all steps in F.V.
2. Draw T.V.
1. In second step reproduce T.V. such that‘d’
is 25 mm in front of FRP.(because corner ‘d’
is 25 mm in front of F.R.P.)
2. Draw F.V. by using vertical and horizontal
projectors.
1. In third step, draw F.V. such that side ab
is making 300 to xy line (edge ab is making
an angle 300 to HRP)
2. Draw TV by using vertical and
horizontal projectors.
M S Shinge
Projections of planes
8
8 A semicircular plate at has the 80 mm diameter straight edge in VP and inclined at 450 to HP. The surface of plate makes an angle of
300 to VP. Draw its projection.
Initial Position: 1) A semicircular plate has a
straight edge in VP. True shape will appear
in FV. Draw semicircle in FV. Straight edge
should be vertical as it is in VP.
Second position: 1) Surface makes an angle
of 300 to VP. Draw TV according to this
inclination. 2) Draw FV by using vertical
and horizontal projectors.
Final position: 1) Straight edge makes an
angle of 450 to HP. Draw a line 450 to XY
line, mark straight edge (bc) and reproduce
FV from FV in second position.
2) Draw TV by using vertical and horizontal
projectors
M S Shinge
Projections of planes
9
9 Draw the projection of circular plane of negligible thickness of 50 mm diameter resting on HP on a point A on the circumference
with its plane inclined 450 to HP and the top view of the diameter passing through the resting point makes 450 to VP.
Initial Position: 1) A semicircular plate has a
straight edge in VP. True shape will appear in
FV. Draw semicircle in FV. Straight edge
should be vertical as it is in VP.
Second position: 1) Surface makes an angle
of 300 to VP. Draw TV according to this
inclination. 2) Draw FV by using vertical and
horizontal projectors.
Final position: 1) Straight edge makes an
angle of 450 to HP. Draw a line 450 to XY
line, mark straight edge (bc) and reproduce
FV from FV in second position.
2) Draw TV by using vertical and horizontal
projectors
M S Shinge