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CHAPTER 17: PLAN AND ELEVATION
17.1 Key Terms
Orthogonal projection - Unjuran ortogon
Plan - Pelan
Front elevation - Dongakan depan
Side elevation - Dongakan sisi
Full scale - Skala penuh
Solid line - Garis penuh
( used to draw visible edge)
Dashed line - Garis putus-putus
(used to draw invisible edge)
Fine solid line - Garis penuh yang halus
(used to show projection/ construction line)
Orthogonal projection on a
vertical plane as viewed from
the front (X)
Orthogonal projection on a
vertical plane as viewed from
the side (Y)
Orthogonal projection on a
vertical plane as viewed from
the top
X
Y
Plans and elevations 1
Orthogonal projection on a
vertical plane as viewed
from the front (X)
Orthogonal projection ona vertical plane as viewed
from the side (Y)
Orthogonal projection on a
vertical plane as
viewed from the top
y
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17.1 Questions according to examination format
Example :
(a)Diagram (i) below shows a solid consisting of a right prism and a right pyramid which are
joined at the plane, PQRS. The base, JKLM, is placed on horizontal plane. PJKQ is the uniform
cross-section of the prism. PJ and SM are vertical edges. The height of the pyramid is
4 cm. Draw the full-scale elevation of the solid on the vertical plane parallel to JK as viewed fromX.
(b) A solid cuboid is joined to the solid in Diagram (i) at the vertical plane, LMSR. The
combined solid is shown in Diagram (ii). The square base, JKED, is on a horizontal plane.
Draw the full-scale
(i) the plan of the combined solid,(ii) elevation of the combined solid on a vertical plane parallel to LE as viewed from Y
Solution
(a) (b)(i) (b)(ii)
Plans and elevations 2
V
Q/R P/S
K/LJ/M5 cm
3 cm
4 cm
Diagram (i)
Diagram (ii)
G/DH/S/M
F/E
P/J
3 cm
4 cm 1 cm
2 cm
V
K
F/G
E/D
4 cm
1 cm
4 cmK/J
I/H
V
R/SQ/P
3 cm
L/M
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1a
Y
1 cm
7 cm
4 c m
3 c m
5 c m
A
E
D C
B
P
H
G
F
T
R
Q
W
V
U
The above diagram shows a solid which consists of two prisms whose base ABPQRCD
lies on a horizontal table. PU = CV = 6 cm and W is the mid-point of PU. The length of PQ
is 7 cm. Draw to full scale, the elevation of the solid on a vertical plane parallel to QR as
viewed from Y.
1b
X1 cm
7 cm
4 c m
3 c m
2 c m
5 c m
A
E
D C
B
P
H
G
F
T
S
R
Q
W
V
U
A semi-cylinder is joined to the solid.
Draw to full scale,
i. the plan of the solid
ii. the elevation the solid on a vertical plane parallel to DR as viewed from x
Plans and elevations 3
Diagram 1(i)
Diagram 1(ii)
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2(a). Diagram 2 (i) shows a solid right prism with the rectangular base, PQRS, resting on ahorizontal table. EFGHQP is the uniform cross section of the prism. Rectangle EFLM is an
inclined plane. Rectangle GHJK is a horizontal plane. EP, FG and HQ are vertical edges.
Draw the full scale plan of the solid.
2(b) A solid cuboid is joined to the prism in Diagram 2(i) at the vertical plane, MSUZ. The
combined solid is shown in Diagram 2(ii) . The base PQRUVWS, is on a horizontal plane and
AB = BC = 2 cm.
Draw the full scale
(i) elevation of the combined solid on a vertical plane parallel to PQ as viewed from X(ii) elevation of the combined solid on a vertical plane parallel to QR as viewed from Y
Plans and elevations 4
Diagram 2 (i)
Diagram 2(ii)
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3(a) Diagram 3(i) shows a solid prism with its rectangular base, PQRS, on a horizontal table.The surface, FGKLRQ, is the uniform cross-section of the prism. Rectangle EFGH is an inclined
plane and rectangle JKLM is a horizontal plane. FQ, KG and LR are vertical edges.
Draw the full scale elevation of the solid on a vertical plane parallel to QR as viewed from X.
3(b) A solid right prism with the uniform cross-section, ITU, is removed from the solid in
Diagram 3(i) . The remaining solid is shown in Diagram 3(ii). Rectangle TFVU is a horizontal
plane. IU is a vertical edge. FT = 3 cm and IU = 2 cm.
Draw the full scale
(i) plan of the remaining solid(ii) elevation of the remaining solid on a vertical plane parallel to PQ as viewed from Y.
Plans and elevations 5
Diagram 3(i)
Diagram 3(ii)
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17.7 Past Year SPM Questions
November 2003
1(a) Diagram 1(i) shows a solid right prism with rectangular base FGPN on a horizontal
table. EFGHHJK is the uniform cross-section of the prism. Rectangle EKLM is an inclined
plane. Rectangle JHQR is a horizontal plane. EF,KJ and HG are vertical edges.
Draw to full scale the plan of the solid . [3 marks]
(b) A solid cuboid is joined to the prism in the Diagram 1(i).at the vertical plane PQRLMN. The
combined solid is as shown in the Diagram 1(ii). The square base FGSW is horizontal.
Draw full scale
(i) the elevation of the combined solid on a vertical plane parallel to FG as viewed from C,
[ 4 marks ]
(ii) the elevation of the combined solid on a vertical plane parallel to GPS as viewed from D.[5 marks ]
Plans and elevations 6
Diagram 1(i)
Diagram 1(ii)
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July 2004
2(a) Diagram 4(i) shows a solid right prism with rectangular base ABCD on a horizontal table.
The surface ABLKGF is the uniform cross section of the prism. Rectangle EFGH is an
inclined plane and rectangle JKLM is a horizontal plane. AF, GK and BL are vertical edges
and GK = 2 cm.
Draw full scale, the elevation of the solid on a vertical plane parallel to AB as viewedfrom X. [ 3 marks ]
(b) Another solid right prism is joined to the prism in Diagram 4(i) at the vertical plane
CVJQ. The combined solid is as shown in Diagram 4(ii). Quadrilateral PQCW is the
uniform cross section of the prism. rectangle WCRU is an inclined plane and the square
TPWU is a horizontal plane. The base ABRSQD lies on a horizontal table,
KL = JM = 3 cm and GK = 2 cm.
Draw full scale,( i ) the plan of the combined solid [ 4 marks]
( ii ) the elevation of the combined solid on a vertical plane parallel to BCR
as viewed from Y [ 5 marks]
Plans and elevations 7
Diagram 4(i)
Diagram 4(ii)
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November 2004
3(a) Diagram 2(i) shows a solid consisting of a cuboid and a half cylinder which are joined at the
plane HJMN. The base GDEF is on a horizontal plane and HJ=3 cm
Draw to full scale, the elevation of the solid on a vertical plane parallel to DG as viewed from X.
[3 marks ]
(b) A solid right prism is joined to the solid in Diagram 2(i) at the vertical plane ELMW. The
combined solid is as shown in diagram 2(ii). Trapezium PMWU is the uniform cross-sectionof the prism and PQRM is an inclined plane. The base DEUTSWFG is on a horizontal plane
and EU= 2cm
Draw to full scale,
(i) the plan of the combined solid [4 marks](ii) the elevation of the combined solid on a vertical plane parallel to UT
as view from Y [5 marks]
Plans and elevations 8
Diagram 2(i)
Diagram 2(ii)
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July 2005
4(a) Diagram 5(i) shows a solid right prism with rectangular base ABCD on a horizontal table.
The surface ABLKGF is the cross-section of the prism. Rectangle GKJH is an inclined
plane. Rectangles JKLM and EFGH are horizontal planes. AF and BL are vertical edges.
Draw full scale, the plan of the solid [ 3 marks]
(b) Another solid cuboid is joined to the prism in Diagram 5(i) at the vertical plane DPJHE.
The combined solid is as shown in Diagram 5(ii). The base ABBCPQV lies on a horizontaltable.
Draw full scale,
( i) the elevation of the combined solid on a vertical plane parallel to BCas viewed from X, [4 marks]
(ii) the elevation of the combined solid on a vertical plane parallel to AB
as viewed from Y. [5 marks]
Plans and elevations 9
Diagram 5(i)
Diagram 5(ii)
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November 2005
5(a) Diagram 3(i) shows a solid right prism with rectangular base PEFN on a horizontal table.
The surface EFGHJ is the uniform cross section of the prism. Rectangle KJHL is an inclined
plane and rectangle LHGM is a horizontal plane. JE and GF are vertical edges.
Draw full scale, the elevation of the solid on a vertical plane parallel to EF as viewedfrom X . [ 3 marks ]
(b) A solid right prism with uniform cross section UVWX is removed from the solid in
Diagram 3(i). The remaining solid is as shown in Diagram 3(ii) rectangle VSTW is a
horizontal plane. UV and XW are vertical edges. VS=3 cm and SE= 2 cm.
Draw full scale,
(i) the plan of the remaining solid [ 4 marks]
(ii) the elevation of the remaining solid on a vertical plane parallel to PE as viewed from Y .[ 5 marks]
Plans and elevations 10
Diagram 3(i)
Diagram 3(ii)
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July 2006
6. (a) Diagram 7(i) shows a solid right prism with rectangular base ABCD on a horizontal plane.
The surface ABHGF is its uniform cross section. The rectangle EFGK is an inclined
plane and the square GHJK is a horizontal plane.The edges AF and BH are vertical.
Draw to full scale, the elevation of the solid on a vertical plane parallel to AB as viewed
from X . [ 3 marks ]
(b) Another solid right prism is joined to the solid in Diagram 7(i) at a vertical plane CJKL to
form a combined solid as shown in Diagram 7(ii). Trapezium KLMS is its uniform cross section.
The rectangle KSRQ is an inclined plane. The edges KL and SM are vertical. The base
ABCMNPLD is on a horizontal plane.
Draw to full scale,
(i) the plan of the combined solid, [ 4 marks](ii) the elevation of the combined solid on a vertical plane parallel to ME as viewed from Y.
Plans and elevations 11
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[ 5 marks]SPM Nov 2006
7(a) Diagram 8(i) shows a solid right prism. The surface KLSR is its uniform cross section.
The base JKLM is a rectangle on a horizontal plane. The rectangle JKRQ is an inclined plane
and the square QRST is a horizontal plane.
The edges SL and TM are vertical.
Draw to full scale, the elevation of the solid on a vertical plane parallel to LK as viewed
from X . [ 3 marks ]
(b) Another solid right prism is joined to the solid in Diagram 8(i) at the vertical plane KLSG
to form a combined solid as shown in Diagram 8(ii).
The trapezium ABCD is its uniform cross section and AFKB is an inclined plane
The rectangle ADEF is a horizontal plane.
The base JKBCLM is on a horizontal plane. The edge DC is vertical.
Draw to full scale,
(i) the elevation of the combined solid on a vertical plane parallel to JB as viewed from Y
[ 4 marks]
(ii) the plan of the combined solid . [ 5 marks]
Plans and elevations 12
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8 SPM Jul 2007
You are not allowed to use graph paper to answer this question.
(a) Diagram 6(i) shows a solid right prism with rectangular base FGRQ on a
horizontal plane. EFGHJKLM is the uniform cross-section of the prism.
Rectangles EMNP , LKUV and JHST are horizontal planes.
FE , LM , KJ and GH are vertical edges. EM = LK = JH = 2 cm.
Draw full scale, the elevation of the solid on a vertical plane
parallel to FG as viewed from A.
Plans and elevations 13
Diagram 6(i)
[3 marks]
P N
T
U
V
Q
S
R
F
J
E
G
H L
K
M
2 cm
6 cm
5 cm
6 cm
3 cm
3 cm
A
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(b) Another solid right prism is joined to the solid in Diagram 6(i) at the vertical plane
PQRSTUVN . The combined solid is shown in Diagram 6(ii). Right-angled triangle
XYZ is its uniform cross-section of the prism.
The base FGRWQ lies on a horizontal plane and FQW is a straighf line.
Draw to full scale,
(i) the plan of the combined solid,
(ii) the elevation of the combined solid on a vertical plane parallel
to GR as viewed from B .
Plans and elevations 14
[4 marks]
P N
T
U V
Q
S
R
F
J
E
G
H L
K
M
2 cm
6 cm
5 cm
6 cm
3 cm
3 cm
Y
X
Z
W
3 cm
2 cm
B
Diagram 6(ii)
[5marks]
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9 November 2007
You are not allowed to use graph paper to answr this question.
(a) Diagram 7(i) shows a solid right prism with rectanglular base ABCD
on a horizontal plane. The surface ABJHGF is the uniform cross-section of the prism. AF , HG and BJ are vertical edges. Rectangle
JKLH is a horizontal plane and rectangle GMEF is an inclined
plane.
Draw full scale, the plan of the solid.
Plans and elevations 15
[3 marks]
6 cm
5 cm
3 cm
8 cm
7 cm
4 cm
A
M
L
D
C
K
E
F
H
G
B
J
Diagram 7(i)
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(b) A half-cylinder solid of diameter 6 cm is joined to the prism in
Diagram 7(i) at the plane SKLT . The length of SK is 4 cm .
The combined solid is shown in Diagram 7(ii).
Draw full scale,
(i) the elevation of the combined solid on a vertical plane parallel
to AB as viewed from P ,
(ii) the elevation of the combined solid on a vertical plane parallelto BC as viewed from Q .
Plans and elevations 16
[4 marks]
[5 marks]
Diagram 7(ii)
C
A
B
J
K
D
F
LG E
M
T
S
H 4 cm
7 cm8 cm
5 cm
P
Q
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10 Jun 2008
You are not allowed to use graph paper to answr this question.
(a) Diagram 15(i) shows a solid right prism. The rectanglular base ABCD
lies on a horizontal plane. The rectangle ABGF is an inclined plane.Trapezium ADEF is the uniform cross-section of the prism.
The edges DE is vertical .
Draw to full scale, the plan of the solid.
Plans and elevations 17
D
C
E
H 3 cm
3 cm
5 cm
5 cm
G
F
A
4
c
m
[3 marks]
Diagram 15(i)
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(b) Another solid right prism is joined to the solid in Diagram 15(i) at the
vertical plane DCHE . The composite solid is shown in Diagram 15(ii).
Pentagon QPNMR is the cross-section of the prism. PJKN is an
inclined plane and NKLM is a horizontal plane The base ABCSRQDlies on a horizontal plane. The edges RM and QP are vertical.
MN = QD = 2 cm and PQ = 6 cm.
Y
X
Draw to full scale
(i) the elevation of the composite solid on a vertical plane parallel
to RQ as viewed from X ,
(ii) the elevation of the composite solid on a vertical plane parallel
to AB as viewed from Y .
Plans and elevations 18
[4 marks]
[5 marks]
P
L
N
4 cm
K
Q
M
J
D
R
C S
E
H
7 cm
4 cm
5 cm
5 cm
G
F
A
B
Diagram 15(ii)
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11 November 2008
You are not allowed to use graph paper to answr this question.
(a) Diagram 15(i) shows a solid right prism with rectanglular base ABHG
on a horizontal plane.The surface ABCDE is the uniform cross-sectionof the prism. AE and BC are vertical edges. Rectangle DEFK is an
inclined plane and rectangle CDKJ is a horizontal plane.
Draw full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X .
Plans and elevations 19
[3 marks]
D C E
H
3 cm
5 cm
6 cm
8 cm
G
F
A
J
4cm
B
K
Diagram 15(i)
X
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(b) A solid cuboid is cut and removed from the solid in Diagram 15(i).
The remaining solid is shown in Diagram 15(ii). Rectangle QRST is a horizontal plane. SB = 2 cm, UT = 3 cm and ST = 4 cm.
Draw to full scale,
(i) the plan of the remaining solid,
(ii) the elevation of the remaining solid on a vertical plane parallel
to BH as viewed from Y .
Plans and elevations 20
[4 marks]
D
Q
E
H
3 cm
5 cm
6 cm
8 cm
G
F
A
J
4cm
B
K
RS
W U
T
[4 marks]
Y
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ANSWERS
Orthogonal
projection
Plan Front Elevation, X Side Elevation
Y1 1 3cm
3cm
1 3cm
3cm
1 3cm
3cm
2 2 5cm
3cm
24cm
5cm
2
4 cm
3cm
36 cm
3
6cm
5cm
3
6cm
5cm
3 45 cm
44cm
5cm
44cm
5cm
54cm
4cm 5
4cm
5cm
5
4cm
5cm
4 6 5cm
4cm
6
6 c m
4cm
6
6 c m
5 cm
7 5cm
6cm
74cm
5cm
7 6 cm
3cm
Orthogonal
projection
Plan Front Elevation, X Side Elevation
Y1 1 3cm
3cm
1 3cm
3cm
1 3cm
3cm
2 2 5cm
3cm
24cm
5cm
2
4 cm
3cm
36 cm
3
6cm
5cm
3
6cm
5cm
3 45 cm
44cm
5cm
44cm
5cm
Plans and elevations 21
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54cm
4cm 5
4cm
5cm
5
4cm
5cm
4 6 5cm
4cm
6
6 c m
4cm
6
6 c m
5 cm
7 5cm
6cm
74cm
5cm
7 6 cm
3cm
8
6cm
85cm
6cm
8
5 cm
3cm
9 5cm
3cm
9 4 c m
2cm
5cm
9
3 cm
4cm
10
6cm
6cm
2cm
2cm
10
6cm
2cm
4cm
10
6cm
2cm
4cm
11 7cm
3cm
11 7cm
4cm
2cm
6 c m
11
3 cm
6 c m
12 7cm
3cm
12
7cm
4cm
2cm
6 cm
12
6 c m
17.43 Elevation involving hidden sides
1
.
2 3 4
Plans and elevations 22
3
cm5
cm
2
cm
1
cm1
cm
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5 6 7
Plan Front elevation, X Side elevation, Y
1
2
6 cm
8 c m
8 c m
8 cm
5 c m
2cm 2cm
2cm
2 c m
8 cm
8 c m
5 c m
4cm
3 c m
3
6 cm
4 cm
2 cm 3 cm 1 cm
2 cm 4 cm
5
c m
1 cm
3 c m
4 cm
3
c m
2 c m
4
8 cm
2 cm
2 cm
3 cm 5 cm
2 cm
8 cm
4 c m
6 c m
1 cm
4 cm
7
c m
1 c m
1 c
m
2 c m
2 cm
5
Plans and elevations 23
3
2
1
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6
1 a.
Y-elevation
7 c m
5 cm
2 cm1 cm
1 cm
3 cm
b.
Plan
1 cm
8 cm
5 c m
2 cm
c.
X-elevation
8 cm
7 c m
3 c m
3 c m
3 c m
1 cm
2 (a) (b)(i) (b)(ii)
3
Plans and elevations 24
4 cm
4cm
6cm
3cm
4
cm
6cm
2cm
2cm
4 cm 1 cm
4 cm
2 cm
1 cm
3 cm
4 cm
1 cm
3 cm1 cm
1 cm
2 cm
10
cm
4 cm
6 cm
2 cm
6 cm
3 cm3 cm
2 cm
6 cm
2 cm
2 cm
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17.7 SPM past years questions
1) SPM2003(N)
1(b)(i)
1(b) (ii)
Plans and elevations 25
5 cm
X/T
G/P/S
2 cm
5 cm
2 cm
V/U
E/M
F/N/W7 cm
J/R
M,N2 cm
R
Q/P
J
H/G
5 cm
5 cm
2 cm
S/WP/NG/F
X//L/V
Q/R
M
T/U
7 cm
K
H/J
E
2 cm
2 cm
3 cm
5 cm 2 cm
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2 SPM2004(Julai)
(a) (b) (i)
b(ii)
3 SPM2004(Nov)
(a)
Plans and elevations 26
3 cm
6 cm
2 cm
3 cm
5 cm
6 cm
3 cm
2 cm
4 cm
4 cm
6 cm
3 cm
2 cm
2cm
4 cm
3 cm
2 cm
4 cm 2cm
7cm
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(b) (i)
b(ii)
4 SPM 2005(Julai)
(a)
Plans and elevations 27
P Q
R K/J/HL/M/N
D/GU/E/W/F
T/S
3 cm
4 cm
2 cm
2 cm
H/G N/F
J
K/D
M/W
P/U
R/S
L/E
Q/T
3 cm
3 cm
4 cm
5 cm
2 cm
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(b) (i)
(ii)
Plans and elevations 28
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5 SPM 2005(Nov)
(b)(i)
3 b(ii)
Plans and elevations 29
7 cm
8 cm
4 cm
J,K
H,L G,M
E,P F,N
K,P
U,V
S,E
L M,N
X,W
H,T G,F
K U
L,M
P,N
XH,G
V,WS,T
E,F
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6 SPM 2006(Julai)
Plans and elevations 30
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7 SPM 2006(Nov)
Plans and elevations 31
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SPM 2007(Jun)
SPM 2007(Nov)
Plans and elevations 32
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SPM 2008(Jun)
SPM 2008(Nov)