# Area of Trapezoids Contributed by: This pdf includes trapezoid, the base of a trapezoid, height of a trapezoid, and area of a trapezoid and some solved questions for the same.
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8.6 Area of Trapezoids
Goal Recall that the parallel sides of a trapezoid are base, b1
Find the area of called the bases of the trapezoid, with lengths
trapezoids. denoted by b1 and b2. height
The shortest distance between the bases is base, b2
Key Words the height of the trapezoid .
• trapezoid p. 332
• base of a trapezoid p. 332 Suppose that two congruent trapezoids with bases b1 and b2 and
height h are arranged to form a parallelogram as shown.
• height of a trapezoid
b1 b2
h
b2 b1
Student Help The area of the parallelogram is h(b1 1 b2). Because the two trapezoids
are congruent, the area of one of the trapezoids is half the area of the
LOOK BACK parallelogram.
trapezoids, see p. 332.
AREA OF A TRAPEZOID
1
Words Area 5 }}(height)(sum of bases)
2
b1
1
Symbols A 5 }}h(b1 1 b2)
2
b2
EXAMPLE 1 Find the Area of a Trapezoid
Find the area of the trapezoid. 6 in.
Solution 8 in.
1
A 5 }}h(b1 1 b2) Formula for the area of a trapezoid
2
1
5 }}(5)(6 1 8) Substitute 5 for h, 6 for b1, and 8 for b2.
2
1
5 }}(5)(14) Simplify within parentheses.
2
5 35 Simplify.
446 Chapter 8 Polygons and Area
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Area of Trapezoids
Find the area of the trapezoid.
1. 7m 2. 16 ft 3. 8 cm
7m 14 ft 5 cm
12 cm
11 m 10 ft
EXAMPLE 2 Use the Area of a Trapezoid
Find the value of b2 given that the area 9m
of the trapezoid is 96 square meters.
A 5 96 m2
Student Help b2
STUDY TIP Solution
The equation is easier
to solve without the 1
A 5 }}h(b1 1 b2) Formula for the area of a trapezoid
fraction. So, multiply 2
each side by 2 before
distributing. 1
96 5 }}(8)(9 1 b2) Substitute 96 for A, 8 for h, and 9 for b1.
2
192 5 8(9 1 b2) Multiply each side by 2.
192 5 72 1 8b2 Use the distributive property.
120 5 8b2 Subtract 72 from each side.
15 5 b2 Divide each side by 8.
Use the Area of a Trapezoid
A gives the area of the trapezoid. Find the missing measure.
4. A 5 77 ft2 5. A 5 39 cm2 6. A 5 84 in.2
b1 13 in.
8 ft
h 6 cm 8 in.
14 ft 8 cm b2
7. A trapezoid has an area of 294 square yards. Its height is 14 yards
and the length of one base is 30 yards. Find the length of the
other base.
8.6 Area of Trapezoids 447
3. Page 3 of 5
8.6 Exercises
Guided Practice
Vocabulary Check 1. Sketch a trapezoid. Label its height h and its bases b1 and b2.
Skill Check Find the height and the lengths of the bases of the trapezoid.
2. 3. 9 4.
7 11
13 12 10
6 8
3 7 5 19 6
Match the trapezoid with the equation used to find the height.
1 1 1
A. A 5 }}h(5 1 13) B. A 5 }}h(8 1 13) C. A 5 }}h(5 1 8)
2 2 2
5. 5 6. 5 7. 8
h h h
8 5 8 13
Practice and Applications
Extra Practice Area of a Trapezoid Find the area of the trapezoid.
See p. 690. 8. 9. 10.
11 6 7
7 8
16
15 10
24
11. 12. 6.2 13.
14 15
13 19 4.6
8 14 8
4.4
Homework Help 14. You be the Judge A classmate states 6
that if you double the dimensions of the
Example 1: Exs. 8–13 6
Example 2: Exs. 18–22 trapezoid at the right, then its area doubles.
9
448 Chapter 8 Polygons and Area
4. Page 4 of 5
15. Visualize It! Draw three different trapezoids with a height of
5 units and bases of 3 units and 7 units. Then find the areas of
the trapezoids. What do you notice?
Student Help Technology In Exercises 16 and 17, use geometry software.
LOOK BACK ●
1 Draw a trapezoid.
To review the ●
2 Draw the midsegment. B
midsegment of a A
trapezoid, see p. 333. 16. Find the length of the midsegment and F
the height of the trapezoid. Multiply the E
C
two measures. D
17. Find the area of the trapezoid. How does
Exercise 16?
Using Algebra In Exercises 18–20, A gives the area of the
trapezoid. Find the missing measure.
18. A 5 135 cm2 19. A 5 132 in.2 20. A 5 198 m2
b1 7 in. b2
10 cm h 12 m
18 cm 17 in. 15 m
IStudent Help 21. A trapezoid has an area of 50 square units. The lengths of the
ICLASSZONE.COM bases are 10 units and 15 units. Find the height.
HOMEWORK HELP
22. A trapezoid has an area of 24 square units. The height is 3 units
Extra help with problem
and the length of one of the bases is 5 units. Find the length of the
solving in Exs. 21–22 is
at classzone.com
other base.
Bridges In Exercises 23–25, use the following information.
The roof on the bridge below, consists of four sides: two congruent
trapezoids and two congruent triangles.
137 ft 13 ft 2 in.
159 ft
Doe River Covered Bridge in Elizabethton, Tennessee
23. Find the combined area of the two trapezoids.
13 f t 7 in.
24. Use the diagram at the right to find the
combined area of the two triangles.
21 f t
25. What is the area of the entire roof ? Detail of roof
8.6 Area of Trapezoids 449
5. Page 5 of 5
Student Help Windows Find the area of the window.
VISUAL STRATEGY 26. 16 in. 27. 28. 9 in.
To find the area of a 12 in.
complex polygon, you 12 in.
30 in.
can add the areas of 21 in.
32 in. 16 in.
the simpler shapes that 12 in.
make up the polygon,
16 in. 48 in. 20 in.
as shown on p. 410.
Using the Pythagorean Theorem Find the height using the
Pythagorean Theorem and a calculator. Then find the area of
the trapezoid.
29. 28 30. 100 31.
h 17
h 40 91 h
11 25 8
24 35 120
Standardized Test 32. Multiple Choice What is the area of the trapezoid?
Practice X
A 25 in.2 X
B 42 in.2 8 in.
68 in.2 84 in.2 4 in.
X
C X
D
13 in.
33. Multiple Choice What is the area of the trapezoid?
X
F 88 ft2 X
G 128 ft2 16 ft
X
H 152 ft2 X
J 176 ft2 8 ft
6 ft
Mixed Review Finding Area Match the region with a formula for its area. Use each
formula exactly once. (Lessons 8.3 – 8.6)
34. Region 1 A. A 5 s2
1
35. Region 2 B. A 5 }}d1d2 1
2
1 2
36. Region 3 C. A 5 }}bh
2 5
3
1
37. Region 4 D. A 5 }}h(b1 1 b2)
2 4
38. Region 5 E. A 5 bh
Algebra Skills Fraction Operations Add or subtract. Write the answer as a fraction
in simplest form. (Skills Review, p. 658)
3 5 5 2 3 1 4 1
39. }} 1 }} 40. }} 2 }} 41. }} 1 }} 42. }} 2 }}
8 8 9 9 4 12 7 5
450 Chapter 8 Polygons and Area