1. Areas of Trapezoids, Rhombi, and Kites LESSON 11–2

2. Lesson Menu Five-Minute Check (over Lesson 11–1) Then/Now New Vocabulary Key Concept: Area of a Trapezoid Example 1:Real-World Example: Area of a Trapezoid Example 2:Area of a Trapezoid Key Concept: Area of a Rhombus or Kite Example 3:Area of a Rhombus and a Kite Example 4:Use Area to Find Missing Measures Concept Summary: Areas of Polygons

3. Over Lesson 11–1 5-Minute Check 1 A.48 cm B.56 cm C.101.1 cm D.110 cm Find the perimeter of the figure. Round to the nearest tenth if necessary.

4. Over Lesson 11–1 5-Minute Check 2 A.37.9 ft B.40 ft C.43.9 ft D.45 ft Find the perimeter of the figure. Round to the nearest tenth if necessary.

5. Over Lesson 11–1 5-Minute Check 3 A.58 in 2 B.83 in 2 C.171.5 in 2 D.180 in 2 Find the area of the figure. Round to the nearest tenth if necessary.

6. Over Lesson 11–1 5-Minute Check 4 A.9.0 m 2 B.62 m 2 C.5 m 2 D.3.4 m 2 Find the area of the figure. Round to the nearest tenth if necessary.

7. Over Lesson 11–1 5-Minute Check 5 A.11 units; 13 units B.12 units; 14 units C.13 units; 15 units D.14 units; 16 units Find the height and base of the parallelogram if the area is 168 square units.

8. Over Lesson 11–1 5-Minute Check 6 A.2.1 centimeters B.4.2 centimeters C.8.4 centimeters D.16.8 centimeters The area of an obtuse triangle is 52.92 square centimeters. The base of the triangle is 12.6 centimeters. What is the height of the triangle?

9. Then/Now You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites.

10. Vocabulary height of a trapezoid

11. Concept 1

12. Example 1 Area of a Trapezoid SHAVING Find the area of steel used to make the side of the razor blade shown below. Area of a trapezoid h = 1, b 1 = 3, b 2 = 2.5 Simplify. Answer: A = 2.75 cm 2

13. Example 1 A.288 ft 2 B.295.5 ft 2 C.302.5 ft 2 D.310 ft 2 Find the area of the side of the pool outlined below.

14. Example 2 OPEN ENDED Miguel designed a deck shaped like the trapezoid shown below. Find the area of the deck. Read the Item You are given a trapezoid with one base measuring 4 feet, a height of 9 feet, and a third side measuring 5 feet. To find the area of the trapezoid, first find the measure of the other base. Area of a Trapezoid

15. Example 2 Solve the Item Draw a segment to form a right triangle and a rectangle. The triangle has a hypotenuse of 5 feet and legs of ℓ and 4 feet. The rectangle has a length of 4 feet and a width of x feet. Area of a Trapezoid

16. Example 2 Use the Pythagorean Theorem to find ℓ. a 2 + b 2 =c 2 Pythagorean Theorem 4 2 + ℓ 2 =5 2 Substitution 16 + ℓ 2 =25Simplify. ℓ 2 =9Subtract 16 from each side. ℓ=3Take the positive square root of each side. Area of a Trapezoid

17. By Segment Addition, ℓ + x = 9. So, 3 + x = 9 and x = 6. The width of the rectangle is also the measure of the second base of the trapezoid. Example 2 Area of a trapezoid Substitution Simplify. Answer: So, the area of the deck is 30 square feet. Area of a Trapezoid

18. Example 2 Check The area of the trapezoid is the sum of the areas of the areas of the right triangle and rectangle. The area of the triangle is or 6 square feet. The area of the rectangle is (4)(6) or 24 square feet. So, the area of the trapezoid is 6 + 24 or 30 square feet. Area of a Trapezoid

19. Example 2 A.58 ft 2 B.63 ft 2 C.76 ft 2 D.88 ft 2 Ramon is carpeting a room shaped like the trapezoid shown below. Find the area of the carpet needed.

20. Concept 2

21. Example 3A Area of a Rhombus and a Kite A. Find the area of the kite. Area of a kite d 1 = 7 and d 2 = 12 Answer: 42 ft 2

22. Example 3B Area of a Rhombus and a Kite B. Find the area of the rhombus. Step 1Find the length of each diagonal. Since the diagonals of a rhombus bisect each other, then the lengths of the diagonals are 7 + 7 or 14 in. and 9 + 9 or 18 in.

23. Example 3B Area of a Rhombus and a Kite Answer: 126 in 2 Area of a rhombus Step 2Find the area of the rhombus. d 1 = 14 and d 2 = 18 Simplify. 2

24. Example 3A A.48.75 ft 2 B.58.5 ft 2 C.75.25 ft 2 D.117 ft 2 A. Find the area of the kite.

25. Example 3B A.45 in 2 B.90 in 2 C.180 in 2 D.360 in 2 B. Find the area of the rhombus.

26. Example 4 Use Area to Find Missing Measures ALGEBRA One diagonal of a rhombus is half as long as the other diagonal. If the area of the rhombus is 64 square inches, what are the lengths of the diagonals? Step 1Write an expression to represent each measure. Let x represent the length of one diagonal. Then the length of the other diagonal is x. __ 1 2

27. Example 4 Use Area to Find Missing Measures Step 2Use the formula for the area of a rhombus to find x. Area of a rhombus A = 64, d 1 = x, d 2 = x __ 1 2 Simplify. 256= x 2 Multiply each side by 4. 16= xTake the positive square root of each side.

28. Example 4 Use Area to Find Missing Measures Answer:So, the lengths of the diagonals are 16 inches and (16) or 8 inches. __ 1 2

29. Example 4 A.3 yd B.6 yd C.2.1 yd D.7 yd Trapezoid QRST has an area of 210 square yards. Find the height of QRST.

30. Concept 3

31. Areas of Trapezoids, Rhombi, and Kites LESSON 11–2