Page 1 of 5 8.6 Goal Area of Trapezoids Find the area of trapezoids. Recall that the parallel sides of a trapezoid are called the bases of the trapezoid, with lengths denoted by b1 and b2. Key Words The shortest distance between the bases is the height of the trapezoid . base, b1 height base, b2 вЂў trapezoid p. 332 вЂў base of a trapezoid p. 332 вЂў height of a trapezoid Suppose that two congruent trapezoids with bases b1 and b2 and height h are arranged to form a parallelogram as shown. b1 b2 b2 b1 h Student Help LOOK BACK To review more about trapezoids, see p. 332. The area of the parallelogram is h(b1 П© b2). Because the two trapezoids are congruent, the area of one of the trapezoids is half the area of the parallelogram. AREA OF A TRAPEZOID 1 2 Words Area П бЋЏбЋЏ(height)(sum of bases) Symbols b1 1 2 A П бЋЏбЋЏh(b1 П© b2) b2 EXAMPLE 1 Find the Area of a Trapezoid Find the area of the trapezoid. Solution 1 A П бЋЏбЋЏh(b1 П© b2) 2 Polygons and Area Formula for the area of a trapezoid Substitute 5 for h, 6 for b1, and 8 for b2. П бЋЏбЋЏ(5)(14) 1 2 Simplify within parentheses. П 35 Simplify. ANSWER Chapter 8 8 in. 1 2 П бЋЏбЋЏ(5)(6 П© 8) 446 6 in. б®Ј The area of the trapezoid is 35 square inches. Page 2 of 5 Area of Trapezoids Find the area of the trapezoid. 1. 2. 7m 3. 8 cm 16 ft 7m 5 cm 14 ft 12 cm 11 m EXAMPLE 10 ft 2 Use the Area of a Trapezoid Find the value of b2 given that the area of the trapezoid is 96 square meters. A П 96 m2 Student Help STUDY TIP The equation is easier to solve without the fraction. So, multiply each side by 2 before distributing. 9m b2 Solution 1 2 Formula for the area of a trapezoid 1 2 Substitute 96 for A, 8 for h, and 9 for b1. A П бЋЏбЋЏh(b1 П© b2) 96 П бЋЏбЋЏ(8)(9 П© b2) 192 П 8(9 П© b2) Multiply each side by 2. 192 П 72 П© 8b2 Use the distributive property. 120 П 8b2 Subtract 72 from each side. 15 П b2 ANSWER Divide each side by 8. б®Ј 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 П 77 ft2 8 ft 5. A П 39 cm2 6. A П 84 in.2 b1 13 in. 6 cm h 14 ft 8 in. 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 Page 3 of 5 8.6 Exercises Guided Practice Vocabulary Check Skill Check 1. Sketch a trapezoid. Label its height h and its bases b1 and b2. Find the height and the lengths of the bases of the trapezoid. 2. 3. 13 6 3 7 4. 9 7 10 12 5 11 19 8 6 Match the trapezoid with the equation used to find the height. 1 2 1 2 C. A П бЋЏбЋЏh(5 П© 8) 5 7. A. A П бЋЏбЋЏh(5 П© 13) B. A П бЋЏбЋЏh(8 П© 13) 5. 6. 5 1 2 8 h h h 5 8 8 13 Practice and Applications Extra Practice Area of a Trapezoid Find the area of the trapezoid. See p. 690. 8. 9. 11 7 10. 6 7 8 15 16 10 11. 12. 24 6.2 13. 14 13 19 15 4.6 8 14 4.4 Homework Help Example 1: Exs. 8вЂ“13 Example 2: Exs. 18вЂ“22 448 Chapter 8 14. You be the Judge A classmate states that if you double the dimensions of the trapezoid at the right, then its area doubles. Do you agree? Explain your answer. Polygons and Area 6 6 9 8 Page 4 of 5 15. Student Help LOOK BACK To review the midsegment of a trapezoid, see p. 333. 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? Technology In Exercises 16 and 17, use geometry software. 1 в—Џ 2 в—Џ Draw a trapezoid. Draw the midsegment. B A 16. Find the length of the midsegment and F E the height of the trapezoid. Multiply the two measures. C D 17. Find the area of the trapezoid. How does the area compare to your answer for Exercise 16? Using Algebra In Exercises 18вЂ“20, A gives the area of the trapezoid. Find the missing measure. 18. A П 135 cm2 b1 10 cm 18 cm IStudent Help ICLASSZONE.COM HOMEWORK HELP Extra help with problem solving in Exs. 21вЂ“22 is at classzone.com 19. A П 132 in.2 20. A П 198 m2 b2 7 in. h 12 m 17 in. 15 m 21. A trapezoid has an area of 50 square units. The lengths of the bases are 10 units and 15 units. Find the height. 22. A trapezoid has an area of 24 square units. The height is 3 units and the length of one of the bases is 5 units. Find the length of the other base. Bridges In Exercises 23вЂ“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 Page 5 of 5 Student Help Windows Find the area of the window. VISUAL STRATEGY 26. 27. 16 in. To find the area of a complex polygon, you can add the areas of the simpler shapes that make up the polygon, as shown on p. 410. 28. 12 in. 30 in. 9 in. 12 in. 32 in. 12 in. 16 in. 21 in. 16 in. 20 in. 48 in. Using the Pythagorean Theorem Find the height using the Pythagorean Theorem and a calculator. Then find the area of the trapezoid. 29. 30. 28 40 h 31. 100 91 11 24 Standardized Test Practice 35 25 8 120 32. Multiple Choice What is the area of the trapezoid? A Й• C Й• 25 in.2 B Й• D Й• 68 in.2 42 in.2 8 in. 4 in. 84 in.2 13 in. 33. Multiple Choice What is the area of the trapezoid? F Й• H Й• 88 ft2 G Й• J Й• 152 ft2 128 ft2 16 ft 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 вЂ“ 8.6) 34. Region 1 A. A П s2 35. Region 2 B. A П бЋЏбЋЏd1d2 36. Region 3 C. A П бЋЏбЋЏbh 37. Region 4 D. A П бЋЏбЋЏh(b1 П© b2) 1 2 Algebra Skills 3 8 Chapter 8 2 5 3 1 2 4 E. A П bh Fraction Operations Add or subtract. Write the answer as a fraction in simplest form. (Skills Review, p. 658) 5 8 39. бЋЏбЋЏ П© бЋЏбЋЏ 450 1 1 2 38. Region 5 Polygons and Area 5 9 2 9 40. бЋЏбЋЏ ПЄ бЋЏбЋЏ 17 h h 3 4 1 12 41. бЋЏбЋЏ П© бЋЏбЋЏ 4 7 1 5 42. бЋЏбЋЏ ПЄ бЋЏбЋЏ

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