Download Shapes and Space Unit Review Answer Section

Shapes and Space Unit Review
Answer Section
The surface area of the composite object is 2650 cm2.
The surface area of the composite object is 1796 cm2.
The surface area of the building is 9200 m2.
The surface area of the composite object is 2784 cm2.
The total surface area of the wooden block is 6400 cm2.
The area that needs to be painted is about 1472 m2.
The surface area of the object is about 560 cm2.
The surface area of the barn is about 936 m2.
The surface area of the object is about 1526 cm2.
The surface area of the object is about 1561 cm2.
The frosted area of the cake is about 2117 cm2.
The frosted area of the cake is about 2425 cm2.
The surface area of the object is about 1657 cm2.
The surface area of the object is about 1400 cm2.
The area that needs to be painted is about 1061 m2.
The scale factor is 2.
The scale factor is 3.5.
Trapezoids C and D
14.62 cm
8 cm, 8 cm, 11.4 cm, and 16 cm
61.25 cm by 50.05 cm
The scale factor is 2.5.
Rectangle B; scale factor is 2.
Rectangle C; scale factor is 1.5.
24. Yes, PQR is a scale diagram of ABC.
The scale factor is 2.
25. a)
The scale factor is 2.
b) 128
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
26.
27.
28.
29.
3
= 0.375
8
30. Triangle Q is a reduction of triangle P; the scale factor for the reduction is
31. a)
.
b)
c)
32. 105 cm
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
26 cm by 12 cm
0.007
0.45
x = 147°
y = 64°
x = 28 cm
The width is 4.5 m.
3.8 cm
x = 20.4
y° = 31°
PQ = 6.72 cm
y=4
x° = 64°
circle, square
A = P, B = Q, C = R
46.
47. EF = 32.4
48. BD = 8
49. CD = 6
CE = 4
50. QR = 15
51. RS = 117.6 m
52. 77 m
53. 7.2 m
54. 10.4 cm
55. a) 2
b) 4
56. Sample answers:
Rectangle: 2 lines of symmetry
Rhombus: 2 lines of symmetry
Square: 4 lines of symmetry
57.
58.
y
5
4
3
2
1
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
x
1
2
3
4
5
6 x
59.
y
6
5
4
3
2
1
60.
y
6
5
4
3
2
1
61. Pentagon P is the reflection image of the black pentagon in the vertical line through 3 on the x-axis.
Pentagon Q is the reflection image of the black pentagon in the horizontal line through 3 on the y-axis.
Pentagon R is the reflection image of the black pentagon in the oblique line through
(4, 10) and (12, 2).
Pentagon S is the reflection image of the black pentagon in the vertical line through 7.5 on the x-axis.
62. Quadrilateral B is the reflection image of quadrilateral A in the oblique line through (0, 8) and (8, 0).
Quadrilateral C is the reflection image of quadrilateral A in the vertical line through 4 on the x-axis.
Quadrilateral D is the reflection image of quadrilateral A in the oblique line through (0, 0) and (8, 8).
63.
y
6
S
5
R
S'
4
3
Q
2
1
P
P'
1
2
3
4
5
6
7
8
9 10
x
The shape PSS'P'Q has coordinates: P(0,1), S(2,5), S'(8, 5), P'(10, 1), Q(5, 3)
64.
a)
4
y
R
3
2
Q
S
1
P
T
–4 –3 –2 –1
–1
Q'
–2
1 2
S'
3
4
–3
–4
R'
b) 4
65. 7
66.
B'
A'
B"
A
C
B
A"
x
P
67.
68.
P
A
69.
70.
71.
72.
6; 60°
4; 90°
180° about the point (3, 1)
a)
A
b) It does not have rotational symmetry.
73. Sample answers:
Rotate the square 90° clockwise about the centre.
Rotate the square 90° counterclockwise about the centre.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
Rotate the square 270° clockwise about the centre.
Rotate the square 270° counterclockwise about the centre.
Rotate the square 180° about the centre.
Rotate the square 360° about the centre.
Sample answers:
90° clockwise about the point (4, 4)
90° counterclockwise about the point (4, 4)
270° clockwise about the point (4, 4)
270° counterclockwise about the point (4, 4)
90° clockwise rotation about the centre
Rotational symmetry of order 4 about the centre
4 lines of symmetry through the centre
5 lines of symmetry
Figure iii
Triangles A and B
The two octagons are related by line symmetry (the vertical line through 4 on the x-axis) and by rotational
symmetry (a 90° rotation about the point (4, 0)).
The diagram has rotational symmetry of order 4 about the origin and 4 lines of symmetry: the x-axis, the
y-axis, the line through (–4, –4) and (4, 4), and the line through (4, –4) and (–4, 4)
i)
a translation R4
ii) a reflection in the y-axis
iii) a 180° rotation about the origin
i)
There is no line of symmetry.
ii) The line of symmetry is the horizontal line through 6 on the y-axis.
iii) The line of symmetry is the vertical line through 4 on the x-axis.
iv) The line of symmetry is the horizontal line through 7 on the y-axis.
The diagram formed by ABC and A'B'C' has two lines of symmetry, the x-axis and the y-axis, and
rotational symmetry of order 2 about the origin.
She is not correct. Neither digit has line symmetry, but 5 has rotational symmetry of order 2.
AC
90°
Answers will vary. For example:
O
P
or
O
P
Q
P
P
O
89.
or
O
Q
90.
Yes.
V
U
O
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
101.
v° = 65°, w° = 35°
a° = 63°, b° = 56°
s = 20.6, t = 37.2
m = 63.4, n° = 60°
d = 24.1, e° = 28°
DE
WX = XY
x° = 61°, y° = 29°
c° = 34°, d° = 112°
Answers may vary. For example:
H
7
14
a
O
6
K
J
102. Answers may vary. For example:
W
4
3
s
6
X
O
4
Y
103. n = 4
104. m = 10.6
105. a = 3
D
Minor arc CD
Major arc CD
C
106.
107.
Inscribed angle
108.
, or
109. Inscribed angle:
Central angle:
110.
111. 180°
112. y° = 68°, z° = 136°
113. c° = 43°, b° = 44°
114. a° = 39°, c° = 51°