a)
The area of triangle ENPF is half the area of rectangle
Amount of Diesel (r gallons)
25
23
21
19
17
Distance Traveled (s miles)
0
24
48
72
96
b)
From the graph, 20 gallons of diesel were left.
c)
The truck uses 1 gallon for every 12 miles
traveled.
Distance 5 number of gallons left · mileage
ANPD.
The area of triangle MNP is equal to the area of
rectangle ENPF.
The area of triangle MNP is half the area of
rectangle ANPD.
Area of triangle MNP 5
The truck can travel 228 miles before it runs
d)
1. Base 5 5 units
Height 5 8 units
From the graph, r , 21.
Area 5
1
2
1
bh
Chapter 10
5
Quick Check
5 20 units2
5 120 m2
The area of the rectangle is 120 square meters.
2. Area of the square 5 10 3 10
5 100 cm2
The area of the square is 100 square centimeters.
3. Rhombus; RU || ST; SR || TU
4. Parallelogram; EF || HG; EH || FG
5. Trapezoid; JM || KL
·3·6
Guided Practice
out of diesel.
1. Area of rectangle 5 15 3 8
2
5 9 square units
5 19 · 12
5 228 mi
1
2.
2
·5·8
Base 5 3 units
Height 5 4 units
Area 5
5
1
2
1
2
bh
·3·4
5 6 units2
3. Base 5 2.1 cm
Height 5 1.8 cm
Area of triangle ABC 5
Lesson 10.1
Hands-On Activity (Prove the Formula for
Finding the Area of a Triangle)
5
2
1
2
bh
· 2.1 · 1.8
5 1.89 cm2
4. Base 5 3.4 ft
Triangle PQR:
Step 3:
Height 5 2.7 ft
Area of rectangle EQRF 5 8 · 2
Area of triangle PQR 5
5 16 square units
© Marshall Cavendish International (Singapore) Private Limited.
1
Area of rectangle AQRD 5 8 · 4
5 32 square units
The area of rectangle EQRF is half the
area of rectangle AQRD.
The area of triangle PQR is equal to the area of
rectangle EQRF.
5
1
2
1
2
bh
· 3.4 · 2.7
5 4.59 ft2
5. Area of triangle JKL 5
35 5
1
2
1
2
bh
·7·h
35 5 3.5 · h
The area of triangle PQR is half the area of
rectangle AQRD.
35 4 3.5 5 3.5h 4 3.5
10 5 h
Area of triangle PQR 5
1
2
·8·4
The height of triangle JKL is 10 meters.
5 16 square units
Triangle MNP:
Step 2:
Area of rectangle ENPF 5 3 · 3
5 9 square units
Area of rectangle ANPD 5 6 · 3
5 18 square units
(M)MIF_P6_SK_Ch07-14 & CR4-14.indd 109
Solutions Key Course 1
109
8/22/11 12:29 PM
6. Area of triangle LMN 5
36 5
1
2
1
2
6. Answers vary. Sample:
bh
b
·b·8
J
L
36 5 4 · b
36 4 4 5 4b 4 4
95b
The base of triangle LMN is 9 inches.
1
7. Area of triangle PQR 5
2
1
19.2 5
2
1
19.2 5
2
h
bh
· b · 9.6
· 9.6 · b
K
7. Area of triangle 5
19.2 5 4.8 · b
19.2 4 4.8 5 4.8b 4 4.8
45b
The base of triangle PQR is 4 centimeters.
5
Practice 10.1
2. Answers vary. Sample: base: QR; height: PS
3. Answers vary. Sample:
b
5
· 25 · 4
2
1
bh
2
1
· 15.5 · 6
2
5 46.5 cm2
9. Area of triangle 5
A
bh
2
1
5 50 cm2
8. Area of triangle 5
1. Answers vary. Sample: base: BC; height: AB
1
76 5
1
bh
2
1
· 15.7 · h
2
76 5 7.85h
h
h5
B
76
7.85
h  9.68
C
h  9.7 in.
10. Area of triangle 5
4. Answers vary. Sample:
D
76 5
1
2
1
2
bh
· 9.3 · h
76 5 4.65h
E
h5
F
76
4.65
h  16.34h
b
h  16.3 in.
5. Answers vary. Sample:
I
11. Area of triangle 5
45 5
1
2
1
2
bh
· b · 7.2
45 5 3.6b
h
G
b
H
b5
45
3.6
b 5 12.5 cm
12. Area of triangle 5
45 5
1
2
1
2
bh
· b · 16.6
© Marshall Cavendish International (Singapore) Private Limited.
h
45 5 8.3b
b5
45
8.3
b  5.42
110
Solutions Key Course 1
(M)MIF_P6_SK_Ch07-14 & CR4-14.indd 110
b  5.4 cm
8/22/11 12:29 PM
13. Area of triangle 5
45 5
1
2
1
2
bh
Area of third triangle 5
5
· b · 7.5
45 5 3.75b
b5
5
45
45 5
2
1
2
2
· (24 2 12) · 10
· 12 · 10
5 area of rectangle 2 area of first triangle 2 area
bh
of second triangle 2 area of third triangle
5 816 2 288 2 204 2 60
· b · 15
5 264 cm2
45 5 7.5b
b5
2
1
bh
Area of shaded region
b 5 12 cm
14. Area of triangle 5
2
1
5 60 cm2
3.75
1
1
18. Area of top shaded triangle 5
45
7.5
5
b 5 6 cm
1
2
1
2
Base of shaded triangle 5 40 2 7
Area of bottom shaded triangle 5
5 33 m
Area of shaded region 5
5
1
2
1
· 33 · 20
2
16. Area of bottom triangle 5
5
1
2
1
2
bh
· 10 · 12
5 60 in.2
5
1
2
1
2
1
2
5
bh
5 330 m2
5
· 24 · 12
shaded triangle
5 72 1 144
5 216 ft2
19. Area of big shaded triangle 5
· 24 · (12 2 5)
1
2
1
2
bh
· 6 · 12
5 36 cm2
Area of small shaded triangle 5
5
Area of shaded region
5 60 1 84
2
bh
5 area of top shaded triangle 1 area of bottom
5
5 area of top triangle 1 area of bottom triangle
2
1
Area of shaded region
bh
· 24 · 7
1
5 144 ft2
5 84 in.2
© Marshall Cavendish International (Singapore) Private Limited.
· 6 · 24
5 72 ft2
15. Area of rectangle 5 lw
Area of top triangle 5
bh
1
2
1
2
bh
·6·6
5 18 cm2
Area of shaded region
5 area of big shaded triangle 1 area of small
5 144 in.2
shaded triangle
17. Area of rectangle 5 lw
5 (10 1 24) · 24
5 34 · 24
5 36 1 18
5 54 cm2
5 816 cm2
Area of first triangle 5
5
1
2
1
2
bh
· 24 · 24
5 288 cm2
Area of second triangle 5
5
1
2
1
2
bh
· 12 · 34
5 204 cm2
Solutions Key Course 1
(M)MIF_P6_SK_Ch07-14 & CR4-14.indd 111
111
8/22/11 12:29 PM
20.
23.
y
8
7
6
5
4
3
2
1
y
A
6
5
4
3
2
N (2, 0) 1
M
B
0
C
x
1 2 3 4 5 6 7 8 9
1
Area of triangle ABC 5
2
1
5
2
1
Area of triangle MNP 5
2
1
bh
17.5 5
·4·6
2
1 2 3 4 5 6
x
bh
·b·5
17.5 5 2.5 · b
5 12 units2
17.5 4 2.5 5 2.5b 4 2.5
The area of triangle ABC is 12 square units.
21.
P (5, 0)
109 876 54 3 2 1 0
75b
b 5 7 units
y
The coordinates of point P are (5, 0).
4 3 2 1 0
24.
D
y
3
2
1
F
1 2 3 4 5 6 7
1
Area of triangle DEF 5
2
1
5
2
76 54 3 2 1 0
1
2
Y
3
4
5
x
Area of triangle XYZ 5
·9·5
5
The area of triangle DEF is 22.5 square units.
Z
1
2
1
2
bh
·6·7
5 21
y
J
x
1 2
bh
5 22.5 units2
22.
X
The area of triangle XYZ is 21 square units.
y
25.
3
2
1
654 3 2 1 0
1
2
3
1 2 3 4 5 6
K
P
x
L
Q
7
6
5
4
3
2
1
Area of triangle JKL 5
5
1
2
1
2
bh
1 2 3 4 5 6
x
·4·4
5 8 units2
The area of triangle JKL is 8 square units.
112
54321 0
R
© Marshall Cavendish International (Singapore) Private Limited.
E
8
7
6
5
4
3
2
1
Area of triangle PQR
59·52
1
2
·4·22
1
2
·9·12
1
2
·5·7
Solutions Key Course 1
(M)MIF_P6_SK_Ch07-14 & CR4-14.indd 112
8/22/11 12:29 PM
1
1
2
2
5 45 2 4 2 4 2 17
Sum of the bases 5 3 1 7
5 19
Area 5
The area of triangle PQR is 19 square units.
26. Area of shaded region
5 56 · 28 2
1
2
· (56 2 24) · 28 2 24 · 28
5 1,568 2 448 2 672
5
1
2
1
2
5 10 units
h(sum of bases)
· 3 · 10
5 15 units2
8. Height 5 4 units
Sum of the bases 5 1 1 3
5 448 ft2
27. ZB 5
3
5 4 units
· 35
7
Area 5
5 15 cm
5
Area of shaded region
1
5 152 +
2
1
2
1
2
h(sum of bases)
·4·4
5 8 units2
· 15 · 35
9. Height 5 7 units
Sum of the bases 5 7 1 4
5 225 + 262.5
5 11 units
5 487.5 cm
2
28. Area of unshaded region
5
1
2
· 10 · 22 1
1
2
Area 5
· 14 · 22
5
5 110 1 154
5 264 in.
Unshaded region → 1 2
7
12
5
3
1
2
5
5 369.6 in.2
· 3 5 8 ft
Area 5
5
· 8 · 8 2 (2 · 3 · 3) 2
1
2
· (8 1 6) · 2
2
1
2
5 8 units
h(sum of bases)
·7·8
11. Height 5 39 ft
Sum of the bases 5 25 1 13 5 38 ft
Area 5
5 32 ft
2
5
© Marshall Cavendish International (Singapore) Private Limited.
1
5 28 units2
5 64 2 18 2 14
Lesson 10.2
Guided Practice
1
2
1
2
h(sum of bases)
· 39 · 38
5 741 ft2
12. Height 5 13 cm
1. Base 5 4 units
2. Base 5 3 units
Height 5 7 units
Height 5 7 units
Area 5 bh
Area 5 bh
54·7
53·7
5 28 units2
5 21 units2
3. Base 5 4 units
4. Base 5 2 units
Height 5 8 units
Height 5 8 units
Area 5 bh
Area 5 bh
54·8
Sum of the bases 5 10.6 1 21
Area 5
5
1
2
1
2
5 31.6 cm
h(sum of bases)
· 13 · 31.6
5 205.4 cm2
52·8
5 32 units
2
5. Base 5 21 cm
5 16 units2
6. Base 5 24 in.
Height 5 12 cm
Height 5 14.5 in.
Area 5 bh
Area 5 bh
5 21 · 12
5 24 · 14.5
5 252 cm2
5 348 in.2
7. Height 5 3 units
(M)MIF_P6_SK_Ch07-14 & CR4-14.indd 113
· 7 · 11
Sum of the bases 5 3 1 5
12
7
Area of shaded region
5 2·
2
h(sum of bases)
10. Height 5 7 units
5
Area of shaded region 5 264 ·
8
2
1
5 38.5 units2
2
29. FH 5 EL 5
1
Solutions Key Course 1
113
8/22/11 12:29 PM
13. Area of trapezoid ABCD
5
5
5
5
1
2
1
2
1
2
1
2
4. Answers vary. Sample:
U
h(b1 1 b2)
· h · (22 1 38)
M
T
· h · 60
· 60 · h
b
h
N
5 30h
Since area of trapezoid 5 1,248 cm2,
30h 5 area of trapezoid
30h 5 1,248
h 5 1,248 4 30
5 41.6 cm
Height of trapezoid 5 DC
5 41.6 cm
Area of triangle ABD 5
5
1
2
1
bh
2
5. Base 5 28 in.
Height 5 15 in.
Area of parallelogram 5
5
5
6. Base 5 18 m
Height 5 10 m
Area of parallelogram 5
The area of triangle ABD is 457.6 square
bh
5 18 · 10
· 22 · 41.6
5 457.6 cm2
bh
28 · 15
420 in.2
5 180 m2
7.
b1
centimeters.
Practice 10.2
h
1. Answers vary. Sample:
A
D
b2
8.
h
h
b1
b2
C
B
2. Answers vary. Sample:
W
9.
Z
b2
h
h
X
b1
10.
Y
b
b1
3. Answers vary. Sample:
b2
P
S
h
11. Area of trapezoid 5
h
5
Q
b
114
R
Solutions Key Course 1
(M)MIF_P6_SK_Ch07-14 & CR4-14.indd 114
5
1
2
1
2
1
2
h(b1 1 b2)
© Marshall Cavendish International (Singapore) Private Limited.
b
· 10 · (15 1 7)
· 10 · 22
5 110 cm2
8/22/11 12:29 PM
1
12. Area of trapezoid 5
5
5
2
1
2
1
2
h(b1 1 b2)
Area of triangle EGH 5
· 17 · (12 1 24)
· 17 · 36
5 306 ft2
5
19.
64
7
1
Q
4 321 0
14. Area of parallelogram 5 bh
64 5 6 · h
42 5
1
2
1
2
· 14 · 14
6
P
5
4
3
2
 9.1 in.
15. Area of trapezoid 5
2
bh
5 98 cm2
64 5 7 · h
h5
2
1
y
13. Area of parallelogram 5 bh
h5
1
64
S
R
1 2 3 4 5 6
x
6
 10.7 in.
Area of parallelogram PQRS 5 5 · 5
h(b1 1 b2)
· h · (5 1 7.5)
5 25 units2
20.
y
42 5 6.25h
h5
2
W
1
42
6.25
h 5 6.72
54 321 0
1
2
3
4
X
Y
5
 6.7 cm
16. Area of trapezoid 5
42 5
1
2
1
2
h(b1 1 b2)
· h · (5.7 1 10)
Z (3, 1)
1 2 3 4
x
42 5 7.85h
h5
42
 5.4 cm
17. Area of trapezoid 5
503.25 5
1
2
1
2
h(b1 + b2)
© Marshall Cavendish International (Singapore) Private Limited.
9.15
5 15 units2
y
21.
· 18.3 · (BC 1 34)
503.25 5 9.15 · (BC 1 34)
503.25
Area of parallelogram WXYZ 5 3 · 5
7.85
E
5 BC 1 34
55 5 BC 1 34
BC 5 55 2 34
BC 5 21 cm
18. Area of trapezoid 5
273 5
273 5
1
2
1
2
1
2
h(b1 1 b2)
4321 0
1
2
3
4
5
H
x
1 2
G
· h · (14 1 25)
· h · (39)
273 5 19.5h
h5
F
5
4
3
2
1
Area of trapezoid EFGH 5
1
2
· 4 · (3 1 8)
5 22 units2
273
19.5
h 5 14 cm
Solutions Key Course 1
(M)MIF_P6_SK_Ch07-14 & CR4-14.indd 115
115
8/22/11 12:29 PM
The area of the pentagon is 110 square
y
22.
centimeters.
2
1
54 321 0
1
2
3
4
B
C
5
4. Area of hexagon 5 55.2 in.2
D (6, 1)
A
1 2 3 4 5 6 7
x
Area of hexagon 5 6 · area of triangle
1
55.2 5 6 · bh
2
1
55.2 5 6 ·
2
·b·4
55.2 5 6 · 2b
55.2 5 12b
1
Area of trapezoid ABCD 5
2
55.2
12
· 5 · (3 1 6)
5 22.5 units2
23. Area of parallelogram PQRT
5b
4.6 5 b
The length of each side of the hexagon
is 4.6 inches.
5 bh
5. Area of hexagonal tile 5 450 4 187.5
5 (5 1 15) · 14.5
5 2.4 ft2
5 20 · 14.5
Area of hexagon 5 6 · area of triangle
5 290 cm2
2.4 5 6 ·
Lesson 10.3
Guided Practice
1
2
2.4 5 6 ·
2.
1
3. Area of triangle 5
5
2
1
2
6
15b
· 6 · 4.1
The length of each side of the hexagon is 1 foot.
6. Area of triangle 5 9.7 · 2
5 5 · 12.3
5 19.4 in.2
Area of octagon 5 8 · area of triangle
5 8 · 19.4
5 61.5 in.
2
The area of the pentagon is 61.5 square inches.
5
2
1
2
· b · 0.8
2.4 5 2.4b
Area of pentagon 5 5 · area of triangle
1
2
2.4 5 6 · 0.4b
bh
5 12.3 in.2
4. Area of triangle 5
1
bh
5 155.2 in.2
The area of the octagon is 155.2 square inches.
7. Area of rhombus 5 12.8 · 2
5 25.6 cm2
· 28 · 24.2
5 338.8 cm2
Area of hexagon 5 3 · area of rhombus
5 3 · 25.6
Area of hexagon 5 6 · area of triangle
5 6 · 338.8
5 2,032.8 cm2
The area of the hexagon is 2,032.8 square
5 76.8 cm2
The area of the hexagon is 76.8 square centimeters.
8. a)
centimeters.
Practice 10.3
1. 8
2.
3. Area of a triangle 5
5
1
2
1
2
12
bh
parallelogram or rhombus
b)
· 8 · 5.5
© Marshall Cavendish International (Singapore) Private Limited.
1. 5
bh
5 22 cm2
Area of pentagon 5 5 · area of triangle
5 5 · 22
trapezoid
5 110 cm
2
116
Solutions Key Course 1
MIF_P6_SK_Ch07-14 & CR4-14_081-164.indd 116
4/29/11 10:17 PM
9. Area of triangle 5
5
1
2
1
2
2. Answers vary. Sample: two trapezoids
bh
· 6 · 9.2
5 27.6 cm2
Area of 5 identical triangles 5 5 · 27.6
5 138 cm2
Area of pentagon 5 5 · area of triangle
1
55·
2
bh
1
55·
3. a)
2
Area of triangle ECD 5 60 in.2
Area of triangle 5
· 6 · 4.1
60 5
5 5 · 12.3
The base of triangle ECD is 10 inches.
b)
Area of square ABCE 5 2
5 102
The area of the figure is 199.5 square centimeters.
10. Area of triangle 5
5
2
1
2
5 100 in.2
bh
The area of square ABCE is 100 square inches.
· 8 · 6.9
c)
5 100 1 60
Area of 6 identical triangles 5 6 · 27.6
5 160 in.2
5 165.6 cm2
The area of trapezoid ABDE is 160 square
Area of hexagon 5 6 · area of triangle
56·
1
2
bh
1
2
inches.
4. a)
Area of parallelogram ABEF 5 bh
84 5 5 · h
· 8 · 6.9
84 4 5 5 5h 4 5
16.8 5 h
5 6 · 27.6
The height of parallelogram ABEF is also the
5 165.6 cm2
© Marshall Cavendish International (Singapore) Private Limited.
Area of trapezoid ABDE
5 area of square ABCE + area of triangle ECD
5 27.6 cm2
56·
· 12 · EC
10 5 EC
5 area of 5 identical triangles + area of pentagon
1
2
bh
60 4 6 5 6 · EC 4 6
Area of figure
5 199.5 cm2
2
1
60 5 6 · EC
5 61.5 cm2
5 138 + 61.5
1
Area of figure
height of triangle BDE.
5 area of 6 identical triangles 1 area of hexagon
Area of triangle BDE 5
5 165.6 1 165.6
5
5 331.2 cm2
The area of the figure is 331.2 square centimeters.
5
5
Lesson 10.4
Guided Practice
1
2
1
2
1
2
1
2
bh
· BD · h
· BD · h
· (12 1 8) · 16.8
5 168 m2
The area of triangle BDE is 168 square
1.
meters.
b)
Area of trapezoid CDEF
1
5 h(b1 + b2)
5
2
1
2
· 16.8 · (5 + 8)
5 109.2 m2
The area of trapezoid CDEF is 109.2 square
meters.
Solutions Key Course 1
MIF_P6_SK_Ch07-14 & CR4-14_081-164.indd 117
117
4/29/11 10:17 PM
Practice 10.4
6. Side length of square 5
36
56m
1.
Area of triangle ABC 5
1
2
·4·6
5 12 m2
Area of parallelogram ABDE
5 36 + 12 + 12
The area of the figure can be found using the
formula for area of a parallelogram, A 5 bh, or by
5 60 m2
7. Answers vary. Sample: I would divide it into two
triangles, ABC and ACD. I would measure the
finding the sum of areas of the two right triangles
lengths of BC, AX, AD, and CY, so that I can find
and the rectangle.
the areas of the two triangles.
2.
A
B
The area of the figure can be found using the
formula for area of a trapezoid, A 5
1
2
Y
h(b1 + b2),
X
or by finding the sum of areas of the two right
C
D
triangles and the rectangle.
3.
8.
180 5 12 · BC 1
1
2
· 12 · 6
180 5 12 · BC + 36
12 · BC 5 144 cm
BC 5
44
12
5 12 cm
The area of the figure can be found using the
formula for area of a trapezoid, A 5
1
2
Area of triangle EBC 5
2
· 12 · 12
5 72 cm2
h(b1 + b2),
or by finding the sum of areas of the right triangle
1
y
9. a)
and the rectangle.
P
3
2
1
54321 0
1
Q 2
3
4
5
R
6
sum of areas of the triangle and rectangle
5. Answers vary. Sample:
b)
1 2 3 4
x
T
S
Area of figure P QRST 5
1
2
·4·515·3
5 10 + 15
5 25 units
© Marshall Cavendish International (Singapore) Private Limited.
4. Answers vary. Sample:
sum of areas of the trapezoid and triangle
118
Solutions Key Course 1
(M)MIF_P6_SK_Ch07-14 & CR4-14.indd 118
8/22/11 12:29 PM
c)
Since the area of triangle PQV is
2
5
82.5 5 7.5h
the area
82.5
of triangle PQT and the two triangles have
7.5
the same height PQ, the base of triangle
2
PQV is
QV 5
5
2
5
2
5
5
11 5 h
the base of triangle PQT.
Area of triangle BDE 5
QT
5h
1
2
· (6.5 1 6.5) · 11
5 71.5 in.2
1
·5
12. Area of triangle 5 bh
2
5 2 units
5
y
1
2
· 28 · 35
5 490 cm2
3
3
2
1
P
8
54321 0
1 2 3 4
1
Q 2
T
V (0,2)
3
4
5
S
R
6
x
· 490 5 183
10. Area of triangle 5
84 5
2
1
2
6
13. Area of triangle SQR 5
12
1.5
1
2
© Marshall Cavendish International (Singapore) Private Limited.
2
cm2.
· 16.5
4.5h 5 24.75
14. BE 5
· 12 · h
BF 5
24.75
4.5
576 5 24 ft
2
3
· 24 5 16 ft
Area of triangle ABF 5
5h
1
2
· 16 · 12
5 96 ft2
Brain@Work
· (2 + 1.5 + 1)
1. Let AP be x ft and PD be 2x ft.
1
Area of trapezoid MNRS
1
2
4
· 9 · h 5 24.75
bh
5 36
5
3
3
5 24.75 in.2
14 5 h
NR 5
cm2
5 5.5 in.
84 5 6h
84
4
The area of the shaded region is 183
h5
1
3
2
· 2x · x 5 49
x2 5
· (36 + 18) · 14
49
x57
5 378 ft2
The area of trapezoid MNRS is 378 square feet.
1
5 PD 2 AP
11. Area of triangle FGE 5 bh
2
26 5
1
2
5 2x 2 x
·b·8
4
5x
5 7 ft
26 5 4b
26
2x 5 14
PS 5 PD 2 SD
Area of figure ABCD 5 (4 ·
5b
b 5 6.5 in.
1
Area of trapezoid BCDE 5 h(b1 + b2)
1
2
· 7 · 14) 1 (7 · 7)
5 196 1 49
5 245 ft2
2
1
82.5 5 h [(6.5 + 6.5) + 2]
2
82.5 5
1
2
· h · 15
Solutions Key Course 1
MIF_P6_SK_Ch07-14 & CR4-14_081-164.indd 119
119
5/3/11 2:19 PM
b)
FG 5 (12 2 x) centimeters
1
Area of shaded region
2
1
5
2
1
· (6 1 12) · 12 2
2
· 12 · AK 5 80
6 · AK 5 80
· 12 · (12 2 x)
AK 5
5 108 2 (72 2 6x)
 13.3 cm
12; triangle
3. Let the side length of ABCD be x.
2
1
1
2
2
· x·x 2
1
1
2
2
· x· x
1
1
1
2
8
2
· (36 1 AD) · 10 5 120 1 180
3
5 · (36 1 AD) 5 300
8
36 1 AD 5
of the square is shaded.
2. Answers vary. Sample: base: NP; height: MQ
3. Area of figure 5
5
2
1
2
The length of AD is 24 centimeters.
10. PR 5
96
8
5 12 ft
bh
UV 5
· 28 · 8
1
2
· 12
5 6 ft
5 112 cm2
The area of the figure is 112 square centimeters.
Area of triangle QUV 5
4. Area of figure 5 35 · 15
2
· (50 1 18) · 31.5
5 1,071 cm
2
6. Area of the shaded region 5
5
1
2
· (32 1 16) · 13.9
5 333.6 cm2
560
Area of hexagon 5 333.6 · 2
16
5 35 in.
The area of the shaded region is 35 square inches.
7. Area of shaded region
2
· 20 · 15 1
1
2
5 667.2 cm2
The area of the hexagon is 667.2 square
centimeters.
· 15 · 15
Chapter 11
Quick Check
5 150 1 112.5
5 262.5 cm
1. 0.451 1 3.12 5 3.571
The area of the shaded region is 262.5 square
2. 0.861 1 6.95 5 7.811
centimeters.
3. 13.74 1 3.791 5 17.531
2
8. a)
Area of parallelogram ABCD 5 16 · 10
5 160 cm2
b)
·6·8
11. Area of trapezoid
2
1
2
The area of triangle QUV is 24 square feet.
The area of the figure is 525 square centimeters.
1
1
5 24 ft2
5 525 cm2
5. Area of figure 5
5
AD 5 24 cm
1. Answers vary. Sample: base: BC; height: AD
1
300
36 + AD 5 60
Chapter Review/Test
5
1.5
5 120 cm2
5 x2
8
· 36 · 10
180
Area of triangle ACD 5
5 x2 2 x2 2 x2
3
2
5 180 cm2
Area of shaded region
5 x2 2 2 ·
1
9. Area of triangle ABC 5
Area of square 5 x2
1
6
5 13.33
5 (36 + 6x) square centimeters
c)
80
4. 5.45 2 1.78 5 3.67
5. 12.795 2 0.816 5 11.979
The area of the parallelogram is 160 square
6. 42.781 2 36.19 5 6.591
centimeters.
7. 1.34 · 9 5 12.06
Area of triangle ACD 5
160
2
5 80
© Marshall Cavendish International (Singapore) Private Limited.
2. a)
8. 4.246 · 2 5 8.492
9. 7.487 · 8 5 59.896
10. 2.56 4 5 5 0.512
120
Solutions Key Course 1
MIF_P6_SK_Ch07-14 & CR4-14_081-164.indd 120
4/29/11 10:17 PM