Shapes and Space Unit Review
1. This object is composed of a cube on top of a right rectangular prism.
Determine the surface area of the object.
10 cm
15 cm
15 cm
30 cm
2. This object is composed of a right rectangular prism attached to the side of a larger right rectangular prism.
Determine the surface area of the object.
11 cm
6 cm
20 cm
13 cm
13 cm
3. This is the floor plan of a building that is 30 m tall with a flat roof.
Determine the surface area of the building, including its roof.
40 m
20 m
4. Three identical right rectangular prisms are glued together to make this composite object.
Determine the surface area of the object.
4 cm
18 cm
20 cm
20 cm
5. This wooden block is in the shape of a cube with side length 30 cm.
A 10-cm square hole is cut through the block.
Determine the total surface area of the block.
6. A shed is open at both ends. The walls and roof will be painted inside and outside.
What is the area that needs to be painted?
16 m
7m
16 m
11 m
7. Determine the surface area of this composite object, to the nearest square centimetre.
The cylinder has diameter 3 cm and height 4 cm.
The prism has length 10 cm, width 9 cm, and height 9 cm.
3 cm
4 cm
9 cm
9 cm
10 cm
8. A barn is built in the shape of a right rectangular prism with a semi-circular roof.
Determine the surface area of the barn. Give your answer to the nearest whole number.
6m
22 m
12 m
9. This object is composed of two identical cylinders connected by a right rectangular prism.
Each cylinder has diameter 18 cm and height 4 cm.
The rectangular prism has length 8 cm and square ends of side length 2 cm.
Determine the surface area of the object. Give your answer to the nearest whole number.
4 cm
18 cm
2 cm
8 cm
10. This object is composed of a right rectangular prism with two congruent triangular prisms attached, one to the
top and the other to bottom.
Determine the surface area of the object, to the nearest square centimetre.
18 cm
5 cm
10 cm
18 cm
11. A two-layer cake is composed of a cylinder on top of a rectangular prism.
The rectangular prism has length 30 cm, width 30 cm, and height 7 cm.
The cylinder has diameter 20 cm and height 6 cm.
The surface of the cake is frosted. What area of cake is frosted?
12. Each layer of a three-layer cake is a cylinder of height 8 cm.
The bottom layer has diameter 28 cm.
The middle layer has diameter 24 cm.
The top layer has diameter 20 cm.
The surface of the cake is frosted. What area of the cake is frosted?
13. This object is composed of three identical cylinders and a right rectangular prism.
Each cylinder has diameter 8 cm and height 5 cm.
The rectangular prism has length 36 cm and square ends of side length 8 cm.
Determine the surface area of the object, to the nearest square centimetre.
5 cm
8 cm
36 cm
8 cm
8 cm
14. A circular hole of diameter 4 cm is cut through this block.
Determine the surface area of the object, to the nearest square centimetre.
15 cm
8 cm
15. A memorial is built using a right rectangular prism of length 17 m, width 20 m, and height 4 m.
The prism is placed on top of four identical cylindrical pillars of diameter 3 m and height 3 m.
The memorial is to be painted on the outside. Determine the area that needs to be painted.
16. Determine the scale factor for this scale drawing.
Original Scale diagram
diagram
17. Determine the scale factor for this scale drawing.
Original
diagram
Scale diagram
18. Which of trapezoids A, B, C, and D are scale diagrams of trapezoid O?
O
A
B
C
D
19. A square has side length 4.3 cm.
The square is enlarged by a scale factor of 3.4.
Determine the side length of the enlargement.
20. An enlargement of the shape below is made using a scale factor of 2.
Determine the side lengths of the enlargement.
4 cm
4 cm
5.7 cm
8 cm
21. A photo has dimensions 17.5 cm by 14.3 cm.
The photo is to be enlarged by a scale factor of 3.5.
Calculate the dimensions of the enlargement.
22. Determine the scale factor for this scale diagram.
Original diagram
Scale diagram
23. Which of rectangles A, B, and C are scale diagrams of the shaded rectangle?
For each scale diagram you identify, state the scale factor.
A
B
C
24. Is PQR a scale diagram of ABC? If yes, state the scale factor.
y
8
Q
6
4
B
2
P
A
0
C
2
4
R
6
8
10
12
14
16
18
x
25. a) Determine the scale factor used to create this pattern of squares.
b) Determine the side length of Square 8.
1
26. Write
2
3
4
as a decimal.
27. A circle has diameter 48 cm. The diameter of the reduction is 42 cm.
Determine the scale factor of the reduction as a fraction and as a decimal.
28. Determine the scale factor of this reduction as a fraction and as a decimal.
Reduction
Original
29. Determine the scale factor of this reduction as a fraction and as a decimal.
Original
Reduction
30. Which two triangles have pairs of corresponding lengths that are proportional?
Identify the scale factor for the reduction.
Q
R
P
31. Determine the scale factor for each reduction.
a) Quadrilateral B is a reduction of quadrilateral A.
b) Quadrilateral C is a reduction of quadrilateral A.
c) Quadrilateral B is a reduction of quadrilateral C.
B
A
C
32. A building is 210 m tall. A scale model is built using a scale factor of 0.005.
Determine the height of the model to the nearest centimetre, if necessary.
33. Draw a reduction of this pentagon using a scale factor of 0.75.
34. A hockey rink measures 52 m by 23 m. A scale diagram is drawn using a scale factor of
Determine the dimensions of the rink in the scale diagram to the nearest centimetre.
35. An airplane is 58 m long. A scale model of the plane is 40.6 cm long.
Determine the scale factor used to create the model as a decimal.
36. Determine the value of y in this proportion:
.
37. These polygons are similar. Determine the values of x° and y°.
147°
x°
64°
y°
38. These quadrilaterals are similar. Determine the value of x.
21 cm
14 cm
x
42 cm
39. A rectangular garden measures 15 m by 9 m.
A similar rectangular garden is 7.5 m long.
Calculate the width of the garden.
40. Rectangle ABCD is similar to rectangle PQRS.
If AB = 7.2 cm, BC = 5.7 cm, and PQ = 4.8 cm, determine the length of QR.
41. These quadrilaterals are similar. Determine the values of x and y°.
13.6
31°
x
15.3
10.2
y°
42. Quadrilateral PQRS is similar to quadrilateral ABCD.
If AB = 3 cm, BC = 4 cm, and QR = 8.96 cm, determine the length of PQ.
43. These parallelograms are similar. Determine the values of x° and y.
B
C
8
A
64°
12
F
E
G
y
x°
6
H
D
44. Any two of which shape will always be similar? Give two examples.
45. Triangle ABC is similar to PQR.
The ratios of the corresponding sides are:
State the corresponding angles.
46. Triangle KLM is similar to RST.
The corresponding angles are: K = R, L = S, M = T
State the ratios of the corresponding sides.
47. Determine the length of EF in these similar triangles.
A
D
9
C
B 16.2
18
F
E
48. Determine the length of BD in these similar triangles.
A
B
C
20
7
D
10.5
E
49. Determine the lengths of CD and CE in these similar triangles.
B
D
8
14
7
C
12
E
A
50. Determine the length of QR in these similar triangles.
Q
T
6
22.5
9
R
S
P
51. Determine the length of RS in these similar triangles.
P
14 m
Q
159.6 m
R
T 19 m
S
Building
52. This scale diagram shows the measurements a surveyor made to determine the height of a building. What is
this height?
33 m
24 m
56 m
53. When the shadow of an electrical tower is 10.8 m long, a 4-m lamp post casts a shadow 6 m long. How tall is
the electrical tower?
54. Determine the length of NO in these similar triangles.
N
L
3.9 cm
M
P 4.8 cm
12.8 cm
O
55. State the number of lines of symmetry in each design.
a)
b)
56. Name two quadrilaterals that have more than 1 line of symmetry.
State the number of lines of symmetry in each quadrilateral.
57. Draw the lines of symmetry in this tessellation.
58. This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape by
drawing its other half.
y
5
4
3
2
1
1
2
3
4
5
6
7
x
59. This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape by
drawing its other half.
y
6
5
4
3
2
1
1
2
3
4
5
6
7
x
60. This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape by
drawing its other half.
y
6
5
4
3
2
1
1
2
3
4
5
6 x
61. Identify the pentagons that are related to the black pentagon by a line of reflection.
Describe the position of each line of symmetry.
y
11
10
9
R
8
7
6
5
4
P
S
3
2
Q
1
1
2
3
4
5
6
7
8
9 10 11 12 13 x
62. This design was created by reflecting quadrilateral A to create quadrilaterals B, C, and D.
Describe the reflections.
y
8
7
6
B
5
4
A
C
3
D
2
1
1
2
3
4
5
6
7
8
x
63. This polygon is one-half of a shape. Use a vertical line through 5 on the x-axis as a line of symmetry to
complete the shape by drawing its other half. Write the coordinates of the larger shape formed by PQRS and
its image.
y
6
S
5
R
4
3
Q
2
1
P
1
2
3
4
5
6
7
8
9 10
x
64. Polygon PQRST is part of a larger shape.
a) Draw the image of polygon PQRST after a reflection in the x-axis.
b) How many lines of symmetry does the larger shape have?
4
y
R
3
2
Q
1
S
P
T
–4 –3 –2 –1
–1
1
2
3
4
x
–2
–3
–4
65. What is the order of rotational symmetry for this design?
66. a) Rotate ABC 90° clockwise about vertex C. Draw the rotation image.
b) Rotate ABC 180° clockwise about vertex C. Draw the rotation image.
A
C
B
67. Draw the rotation image after rotating the shape 90° clockwise about P.
P
68. Draw the rotation image after a 90° clockwise rotation about vertex A.
P
A
69. What is the order of rotational symmetry and angle of rotation symmetry for this design?
O
X
X
O
O
X
X
O
O
X
X
O
70. What is the order of rotational symmetry and angle of rotation symmetry for this design?
71. Hexagon B is the rotation image of hexagon A. Describe the rotation.
4
y
3
2
B
1
A
1
2
3
4
5
6
7
x
72. This polygon is part of a larger shape that is to be completed by a rotation of 90° clockwise about point A.
a) Complete the shape.
b) What is the order of rotational symmetry and angle of rotation symmetry of the larger shape?
A
73. Describe two different rotations that will result in this square coinciding with itself.
74. Describe a rotation that makes parallelogram QRST a rotation image of parallelogram ABCD.
10
y
9
8
T
7
6
Q
B
5
C
4
3
A
D
2
S
1
R
1
2
3
4
5
6
7
8
9
x
75. Describe a rotation that makes circle B a rotation image of circle A.
G
A
H
F
B
G
C
D
F
E
Circle A
H
E
A
B
D
C
Circle B
76. Describe the rotational symmetry and line symmetry of this design.
77. How many lines of symmetry does a regular pentagon have?
78. Which figure below shows two quadrilaterals related by both rotational symmetry and line symmetry?
y
5
Figure i
4
Figure ii
3
Figure iii
2
1
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
7
8
9 10 11 12
x
–2
–3
–4
–5
79. Which of triangles A, B, and C are related to the shaded triangle by rotational symmetry about the origin?
y
5
4
3
2
B
1
–5 –4 –3 –2 –1
–1
C
–2
1
2
3
4
5
x
A
–3
–4
–5
80. Determine whether the two octagons are related by line symmetry, by rotational symmetry, by both types of
symmetry, or by neither.
y
5
4
3
2
1
–1
1
2
3
4
5
6
7
8
x
–2
81. The design below is created after trapezoid ABCD is rotated 90° clockwise about the origin, 180° about the
origin, and 90° counterclockwise about the origin. Identify any symmetry in the design.
y
B
4
C
3
2
1
A
–5 –4 –3 –2 –1
–1
D
1
2
3
4
5
x
–2
–3
–4
82. Describe three different transformations that would make rhombus B the image of rhombus A.
y
3
2
1
A
B
–4 –3 –2 –1
–1
1
2
3
4
x
–2
–3
83. Determine whether polygon A and its image are related by line symmetry after each transformation:
i) a translation R3
ii) a translation U6
iii) a reflection in a vertical line through 4 in the x-axis
iv) a reflection in a horizontal line through 7 in the y-axis
y
13
12
11
10
9
8
7
6
5
4
3
A
2
1
1
2
3
4
5
6
7
8
x
84. Triangle A'B'C' is the image of ABC after a 180° rotation about the origin.
Identify any symmetry.
y
4
3
C'
A
1
–6 –5 –4 –3 –2 –1
–1
B'
B
2
–2
–3
–4
A'
1
2
3
4
5
x
C
85. Marleesa says these digits do not have line symmetry or rotational symmetry. Is she correct? If not, explain
her mistake.
86. O is the centre of this circle.
Which line is a tangent?
A
B
C
O
D
E
87. O is the centre of this circle. Point T is a point of tangency.
What is the value of e°?
T
e°
O
88. Draw a line through point P that is NOT a tangent to the circle.
O
P
89. Draw a line through point P that is a tangent to the circle.
Label the point of tangency Q.
P
O
90. Is the line that passes through points U and V a tangent to the circle?
V
U
O
91. O is the centre of this circle and point B is a point of tangency.
Determine the values of v° and w°.
O
v°
55°
w°
C
B
25°
A
92. O is the centre of this circle and point V is a point of tangency.
Determine the values of a° and b°.
O
a°
b°
34°
27°
W
V
U
93. O is the centre of this circle and point Q is a point of tangency.
Determine the values of s and t. If necessary, give your answers to the nearest tenth.
L
s
M
32
N
28
19
t
O
94. O is the centre of this circle and point S is a point of tangency.
Determine the values of m and n°. If necessary, give your answers to the nearest tenth.
O
n°
39
m
30°
R
S
T
50
95. O is the centre of this circle and point Q is a point of tangency.
Determine the values of d and e°. If necessary, give your answers to the nearest tenth.
R
Q
d
e°
P
21
32
62°
O
96. O is the centre of this circle.
Which line segment is a diameter?
C
E
O
D
G
F
97. O is the centre of the circle.
What can you say about the lengths of WX and XY?
W
X
O
Y
98. O is the centre of the circle.
What can you say about the measure of
B
A
?
C
O
99. Point O is the centre of this circle.
Determine the values of x° and y°.
R
|
y°
O
x°
S
|
29°
T
100. Point O is the centre of this circle.
Determine the values of c° and d°.
c°
d° O
34°
101. Point O is the centre of this circle. Without solving for a, sketch and label the length of any extra line
segments you need to draw to determine the value of a.
H
14
a
O
6
K
J
102. Point O is the centre of this circle. Without solving for s, sketch and label the lengths of any extra line
segments you need to draw to determine the value of s.
W
s
6
X
O
4
Y
103. Point O is the centre of this circle.
Determine the value of n to the nearest tenth, if necessary.
H
10
O
3
n
J
K
104.
Point O is the centre of this circle.
Determine the value of m to the nearest tenth, if necessary.
A
7
O
12
m
B
C
105. Point O is the centre of this circle.
Determine the value of a to the nearest whole number.
H
14
|
F
G
|
a
O
5
K 12
J
106. Label the major arc CD and the minor arc CD of this circle.
D
C
107. O is the centre of this circle. Is
A
C
O
B
a central angle or an inscribed angle?
108. O is the centre of this circle.
What is the relationship between the measures of
and
?
D
E
O
F
109. O is the centre of this circle.
In this circle, identify the inscribed angle and the central angle subtended by the same minor arc.
Q
P
O
R
110. What is the relationship between the measures of
X
W
Y
Z
111. Point O is the centre of the circle. Arc AB is a semicircle.
What is the measure of
?
A
O
B
and
?
112. Point O is the centre of this circle.
Determine the values of y° and z°.
B
A
z°
O
68°
y°
D
C
113. Point O is the centre of the circle.
Determine the values of b° and c°.
J
H
44°
O
b°
43°
c°
L
K
114. Point O is the centre of the circle.
Determine the values of a° and c°.
M
a°
N
O
51°
Q
c°
P