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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.

1.
Page 1 of 5

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.

To review more about

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.

ANSWER © The area of the trapezoid is 35 square inches.

446 Chapter 8 Polygons and Area

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.

To review more about

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.

ANSWER © The area of the trapezoid is 35 square inches.

446 Chapter 8 Polygons and Area

2.
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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.

ANSWER © The value of b2 is 15 meters.

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

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.

ANSWER © The value of b2 is 15 meters.

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

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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.

Do you agree? Explain your answer.

9

448 Chapter 8 Polygons and Area

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.

Do you agree? Explain your answer.

9

448 Chapter 8 Polygons and Area

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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

the area compare to your answer for

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

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

the area compare to your answer for

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

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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

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