Lesson 10.2 Area of Parallelograms and Trapezoids
For each parallelogram, draw and label the height
h
for the given base
b
.
1.
A
C
D
D
b
B
2.
F
E
H
G
b
For each parallelogram, label a base and a height. Use
b
and
h
.
3. 4.
Find the area of each parallelogram.
5.
26 in.
18 in.
6.
23 ft
14 ft
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For each trapezoid, label the height and bases. Use
h
,
b
1
, and
b
2
.
7. 8.
Find the area of each trapezoid.
9.
20 in.
12 in.
15 in.
13 in.
10.
14 cm
18 cm
11 cm
Solve. Show your work.
11. The area of parallelogram EFGH is 207 square inches. Its height is 9 inches.
Find the length of GH.
9 in.
E
H
G
F
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38 Chapter 10 Lesson 10.2
12. The area of parallelogram ABCD is 112 square inches. The length of BC is
16inches. Find the height.
C
B
A
16 in.
D
13. The area of trapezoid PQRS is 108 square centimeters. Find the height.
R
Q
P
10 cm
S
17 cm
14. The area of trapezoid WXYZ is 375 square feet. Find the height.
X
W
Z
Y
30 ft
20 ft
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Solve.
15. Three out of the four coordinates of the vertices of a parallelogram are A (0, 3),
B (3, 2), and D (5, 3). Plot the coordinates on the coordinate plane. Find the
coordinates of point C. Then find the area of parallelogram ABCD.
16. The coordinates of the vertices of a trapezoid are P (4, 1), Q (5, 1), R (3, 4),
andS (0, 4). Plot the coordinates on the coordinate plane. Find the area of
trapezoid PQRS.
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40 Chapter 10 Lesson 10.2
Solve. Show your work.
17. The area of trapezoid JKMN is 136 square miles. Its height is 8 miles. Find the
length of JN.
J
KM
N
20 mi
8 mi
18. Trapezoid ABCD is made up of triangles ABC and ADC. The area of trapezoid
ABCD is 312 square yards. Find the area of triangle ABC.
A
B
C
D
20 yd
28 yd
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146 Answers
23.
x
2
1
2
1
4
3
23 1
44
5321
0
y
G
HK
Area
1
2
3 5 7.5 square units
24. Base of triangle
HKM
64
8 in.
Height of triangle
HKM
144
8 4 in.
Area of triangle
HKM
1
2
8 4 16 in.
2
Area of the gure
144 64 16
224 square inches
25. Length of 1 side:
160 4 40 in.
By observation, triangles
PQM
and
NPS
together make up
1
2
of the square, and
triangle
MNR
make up
1
8
of the square.
1
1
2
1
8
8
8
4
8
1
8
3
8
So, the area of triangle
PMN
is
3
8
the area
of
PQRS
.
Area of triangle
PMN
3
8
40 40
600 square inches
26. Length of the small square
16 12 4 in.
Area of the larger square
4
1
2
16 12 4 4 400 in.
2
Side length of the larger square
400
20 inches
Lesson 10.2
1.
b
A
B
D
C
2.
b
E
G
F
H
3. Answers vary. Sample:
b
h
4. Answers vary. Sample:
b
h
5. 26 18 468 square inches
6. 14 23 322 square feet
7.
h
b
2
b
1
8.
b
2
b
1
h
9.
1
2
12(15 20)
210 square inches
10.
1
2
11(14 18)
176 square centimeters
11. 207 9 23 inches
12. 112 16 7 inches
13. Area
1
2
h
(10 17) 108 cm
2
h 108 2 27
8 centimeters
14. Area
1
2
h
(30 20) 375
h 375 2 50 15 feet
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15.
x
2
1
4
2
3
1
23 1
44
5 6321
0
y
B
AD
C
3
The coordinates of point
C
are (2, 2).
Base 5 units, height 5 units
Area of parallelogram
ABCD
5 5 25 square units
16.
x
2
3
4
5
1
1
2
23 145
4
521
0
y
3
R
S
PQ
RS
3 units,
PQ
9 units,
height 5 units
Area of trapezoid
PQRS
1
2
5(3 9) 30 square units
17.
1
2
8(
JN
20) 136
4(
JN
20) 136
JN
136 4 20 14 miles
18.
1
2
h
(20 28) 312
h 312 2 48
13 yards
Area of triangle
ABC
1
2
20 13 130 square yards
Lesson 10.3
1. 7 triangles
2. 10 triangles
3. Area of a triangle
1
2
17.5 12
105 cm²
Area of the pentagon
5 105
525 square centimeters
4. Area of a triangle
1
2
12 10.3
61.8 in.²
Area of the hexagon
6 61.8
370.8 square inches
5. The pentagon is made up of 5 identical
triangles.
Area of each triangle
292.5 5 58.5 ft
2
1 side of the pentagon
58.5 2
9
13 feet
6. The hexagon is made up of
6 identical triangles.
Area of each triangle
93.6 6 15.6 in.
2
Height of each triangle
15.6 2
6
5.2 in.
Height of the hexagon
5.2 2 10.4 inches
7. Area of the hexagon
3 (7 6)
126 square centimeters
8. Area of a triangle
1
2
8.4 13
54.6 cm²
Area of the polygon
54.6 10
546 square centimeters
9. Area of trapezoid
ABHG
Area of trapezoid
CDEF
1
2
(10 24) 7
119 cm²
Area of rectangle
BCGF
24 10
240 cm²
Area of the polygon
119 119 240
478 square centimeters
10. Area of triangle
OAB
1
2
18 26
234 cm²
Area of the pentagon
234 5
1,170 cm²
Area of triangle
AEF
1
2
42.3 24.7
522.405 cm²
Area of the gure
1,170 522.405
1,692.405 square centimeters