Name
Class
Date
Practice
10-2
Form G
Areas of Trapezoids, Rhombuses, and Kites
Find the area of each trapezoid.
16 ft
1.
10 ft
3.
7.5 m
9 ft
125 ft 2
9m
2.
116.25 m 2
4 yd
7 yd
13 yd
22 m
59.5 yd 2
4. Find the area of a trapezoid with bases 20 cm and 14 cm and height 5 cm. 85 cm 2
5. Find the area of a trapezoid with bases 8 in. and 7 in. and height 5.2 in. 39 in. 2
Find the area of each trapezoid. If your answer is not an integer, leave it in
simplest radical form.
6.
8 in.
11 ft
7.
11 in.
30
10 cm
6 ft
18 in.
13 "21
14 cm
8.
2 ft
48 "2
in. 2
Q 70 2 25 "3 R cm 2
2
ft 2
Find the area of each kite.
9.
6.5 ft
2 ft
3 cm
10.
4 ft
4m
11.
34 ft 2
11 m
3 cm
5 cm
4 ft
6m
6m
3 cm
90 m 2
24 cm 2
12. Find the area of a kite with diagonals 12 ft and 3 ft. 18 ft 2
13. Find the area of a kite with diagonals 16 m and 14 m. 112 m 2
Find the area of each rhombus.
14.
25 ft
15.
8 in.
16.
6m
4m
10 in.
22 ft
1100 ft 2
16 "5 m 2
17. Find the area of a rhombus with diagonals 9 yd and 6 yd. 27
yd 2
10 "39 in. 2
18. Find the area of a rhombus with diagonals 4.5 in. and 5.2 in. 11.7 in. 2
19. Open-Ended Draw a rhombus. Measure the lengths of its diagonals.
Find its area. Check students’ work.
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Name
Class
Date
Reteaching
10-2
Areas of Trapezoids, Rhombuses, and Kites
The area of a trapezoid is 12h(b1 1 b2), where h is the length of the height and
b1 and b2 are the lengths of the two parallel bases.
Problem
12 in.
W
What is the area of trapezoid WXYZ?
X
8 in.
Draw an altitude to divide the trapezoid into a rectangle and
a 308-608-908 triangle. In a 308-608-908 triangle, the length of the
"3
60
Z
longer leg is 2 times the length of the hypotenuse.
"3
h 5 2 (8) 5 4"3 in.
16 in.
W
X
12 in.
4 63 in.
Use the formula for the area of a trapezoid.
A 5 12h(b1 1 b2)
Z
Y
8 in.
60
Y
16 in.
Substitute.
5 12 (4"3 )(12 1 16)
Simplify.
5 56"3 in.2
The area of trapezoid WXYZ is 56"3 in. 2
Find the area of each trapezoid. If necessary, leave your answer in simplest
radical form.
15 in.
1.
12 ft
2.
17 in.
63 ft 2
10 m
4.
5m
3 in.
4.5 ft
7 in.
112 in. 2
3.
5.
16 ft
19.5 in. 2
7m
24 cm
6.
30
4m
45
20 cm
60
75 m 2
8 in.
5 in.
16 "3 m 2
C
D
(240 2 50"3)
cm 2
7. Find the area of a trapezoid with bases 9 m and 12 m and height 6 m. 63 m 2
8. Find the area of a trapezoid with bases 7 in. and 11 in. and height 3 in. 27 in. 2
9. Find the area of a trapezoid with bases 14 in. and 5 in. and height 11 in. 104.5 in. 2
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Name
Class
10-2
Date
Reteaching (continued)
Areas of Trapezoids, Rhombuses, and Kites
The area of a rhombus or a kite is 12d1d2 , where d1 and d2 are the lengths of the
diagonals. The diagonals bisect each other and intersect at right angles.
Problem
What is the area of rhombus ABCD?
7 cm
A
First find the length of each diagonal.
B
x
d1 5 7 1 7 5 14
Diagonals of a rhombus bisect each other.
82 5 72 1 x2
Pythagorean Theorem
64 5 49 1 x2
Simplify.
8 cm
C
D
x 5 "15
d2 5 2x 5 2"15 cm
Use the formula for the area of a rhombus.
A 5 12 d1d2
Substitute.
5 12(14)(2"15)
Simplify.
5 14"15 cm 2
The area of rhombus ABCD is 14"15 cm2.
Find the area of each rhombus. Leave your answer in simplest radical form.
10.
11.
13.5 ft
7 yd
12.
15 ft
3 cm
98 "3 yd 2
60 405 ft 2
18 "3 cm 2
Find the area of each kite. Leave your answer in simplest radical form.
13.
4 ft
9 ft
14.
15.
30
7 yd
9 ft
12 ft
45
60
12
cm
30
2.5 yd
45
23.75 "3
144 ft 2
16. Find the area of a kite with diagonals 13 cm and 14 cm. 91 cm 2
yd 2
(36 1 36"3) cm 2
17. Find the area of a rhombus with diagonals 16 ft and 21 ft. 168 ft 2
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