1. Transparency 5 Click the mouse button or press the Space Bar to display the answers.

2. Transparency 5a

3. 6-4 Areas of Other Figures

4. Geogebra Trapezoid Proof Area of complex Figures Area of a Trapezoid Multiple Areas

5. Video Tutor Help Finding the measure of an angle Finding the area of parallelograms Finding the area of triangles Finding the area of trapezoids Finding circumference Finding the area of circles

6. Video Tutor Help Irregular shape area Circumference of a circle Brain Pop Area of polygons Finding the area of trapezoidsFinding the area of trapezoids (6-4) Finding the area of irregular figures (6-4)Finding the area of irregular figures Area of a Trapezoid Area of a Complex Figure Khan Academy

7. Find surface area of cubes and prisms by pulling them apart Lesson Slides Find surface area of cubes and prisms using formulas Lesson Slides Find missing dimensions using the volume formula Lesson Slides Choose the appropriate measurement for solving a problem Lesson Slides

8. Worksheets Daily Notetaking Guide Worksheets Version A Practice, Guided Problem Solving Lesson 6-4 Practice 6-4 Guided Problem Solving 6-4

9. Vocabulary Practice Vocabulary (Electronic) Flash Cards Percents Vocabulary 6A: Graphic Organizer Vocabulary 6B: Reading Comprehension Vocabulary 6C: Reading/Writing Math Symbols Vocabulary 6D: Visual Vocabulary Practice Vocabulary 6E: Vocabulary C Vocabulary 6F: Vocabulary Review Puzzle

10. Additional Lesson Examples Step-by-Step Examples Lesson 6-4

11. Lesson Readiness Lesson Quiz Problem of the Day Lesson 6-4

16. Trapezoid Proof Area of a Trapezoid

17. B. (–1, 1), (5, 1), (4, 4), (0, 4) = 15 units 2 A = h(b 1 + b 2 ) 1212 = 3(6 + 4) 1212 Area of a trapezoid Substitute for h, b 1, and b 2. (–1, 1) (0, 4) (4, 4) x y (5, 1) Graph and find the area of the figure with the given vertices. Additional Example 3: Finding the Area of Triangles and Trapezoids 6 3 4

18. A. (–1, –2), (5, –2), (5, 2), (–1, 6) Partner Share! Example 3 Graph and find the area of the figure with the given vertices. = 36 units 2 A = h(b 1 + b 2 ) 1212 = 6(8 + 4) 1212 Area of a trapezoid Substitute for h, b 1, and b 2. (–1, –2) (–1, 6) (5, 2) x y (5, –2) 48 6

19. Example 5-3a Find the area of the trapezoid. Area of a trapezoid The height is 6 meters. The bases aremeters and meters. Replace h with 6 and a with and b with. Find Area of a Trapezoid

20. Example 5-3a Divide out the common factors. Simplify. Answer: The area of the trapezoid is square meters.

21. Find the perimeter of the triangle. LESSON 6-4 Perimeter and Area of a Triangle Add the lengths of the legs. 7 + 10 + 14 = 31 ft The perimeter is 31 ft Additional Examples

25. Additional Example 1A: Finding the Area of Composite Figures by Adding Find the total area. Round to the nearest tenth, if necessary. A = bh A = 12 6 A = 72 m 2 8 m area of the rectangle: 2 m 6 m Divide the figure into a rectangle and a trapezoid. 2 m 6 m 12 m 4 m

26. Additional Example 1A Continued Find the total area. Round to the nearest tenth, if necessary. 8 m area of the trapezoid: 2 m 6 m 2 m 6 m A = h(b 1 + b 2 ) 1 2 __ A = 2(4 + 2) 1 2 __ A = (12) 1 2 __ A = 6 m 2 Add the area of the rectangle and the area of the trapezoid. total area: A = 72 + 6 = 78 m 2. 4 m

27. Additional Example 1B: Finding the Area of Composite Figures by Adding Find the shaded area. Round to the nearest tenth, if necessary. A = bh A = 20 8 A = 160 in 2 12 in. area of the rectangle: 20 in. 8 in. Divide the figure into a rectangle and a semicircle. 8 in.

28. area of the semicircle: A = (r 2 ) 1 2 __ A  (3.14 4 2 ) 1 2 __ A  (50.24) 1 2 __ A  25.1 in 2 Additional Example 1B Continued Find the shaded area. Round to the nearest tenth, if necessary. 12 in. 20 in. 8 in. Add the area of the rectangle and the area of the semicircle. total area: A = 160 + 25.1 = 185.1 in 2.

29. A = bh A = 8 9 A = 72 yd 2 area of the rectangle: Partner Share! Example 1A Find the shaded area. Round to the nearest tenth, if necessary. Divide the figure into a rectangle and a triangle. 10 yd 9 yd 8 yd

30. Partner Share! Example 1A Continued Find the shaded area. Round to the nearest tenth, if necessary. area of the triangle: A = bh 1 2 __ A = (2 9) 1 2 __ A = (18) 1 2 __ A = 9 yd 2 Add the area of the rectangle and the area of the triangle. total area: A = 72 + 9 = 81 yd 2 10 yd 9 yd 8 yd

31. Partner Share! Example 1B Find the shaded area. Round to the nearest tenth, if necessary. A = bh A = 22 10 A = 220 m 2 12 m area of the rectangle: 22 m Divide the figure into a rectangle and a semicircle. 10 m

32. area of the semicircle: A = (r 2 ) 1 2 __ A  (3.14 5 2 ) 1 2 __ A  (78.5) 1 2 __ A  39.3 m 2 Partner Share! Example 1B Continued Find the shaded area. Round to the nearest tenth, if necessary. Add the area of the rectangle and the area of the semicircle. total area: A = 220 + 39.3 = 259.3 m 2 12 m 22 m 10 m

33. Additional Example 2: Finding the Area of Composite Figures by Subtracting Find the shaded area. A = bh A = 12 9 = 108 ft 2 Area of the rectangle: Area of the triangle: A = bh 1 2 __ A = (6)(7) 1 2 __ A = 42 = 21 ft 2 1 2 __ Shaded area: Subtract the area of the triangle from the area of the rectangle. A = 108 – 21 = 87 ft 2 5 ft 12 ft 6 ft 9 ft

34. Partner Share! Example 2 Find the shaded area. A = bh A = 16 8 = 128 in 2 Area of the rectangle: Area of the triangle: A = bh 1 2 __ A = (5)(7) 1 2 __ A = 35 = 17.5 in 2 1 2 __ Shaded area: Subtract the area of the triangle from the area of the rectangle. A = 128 – 17.5 = 110.5 in 2 9 in. 16 in. 5 in. 8 in.

35. Additional Example 3: Landscaping Application What is the area of the room floor shown in the figure? Round to the nearest tenth. To find the area, divide the composite figure into a square, a rectangle, and a semicircle. 6 ft 12 ft 18 ft

36. Additional Example 3 Continued A = s 2 A = 6 2 = 36 ft 2 Area of the square: 6 ft 12 ft A = bh A = 18 6 = 108 ft 2 Area of the rectangle: A = r 2 1 2 __ A  3.14 (9) 2 1 2 __ A  (254.34)  127.17 ft 2 1 2 __ Area of the semicircle: 18 ft

37. Additional Example 3 Continued What is the area of the room floor shown in the figure? Round to the nearest tenth. 6 ft 12 ft 18 ft The area of the room is approximately 271.2 ft 2.A = 36 + 108 + 127.17 = 271.17 ft 2 Area of the room:

38. Partner Share! Example 3 What is the area of the stage floor shown in the figure? Round to the nearest tenth. To find the area, divide the composite figure into a square, a rectangle, and a semicircle. 5 ft 10 ft 15 ft

39. Partner Share! Example 3 Continued A = s 2 A = 5 2 = 25 ft 2 Area of the square: 5 ft 10 ft A = bh A = 15 5 = 75 ft 2 Area of the rectangle: A = r 2 1 2 __ A  3.14 (7.5 2 ) 1 2 __ A  (314)  88.3 ft 2 1 2 __ Area of the semicircle: 15 ft

40. Partner Share! Example 3 Continued What is the area of the room floor shown in the figure? Round to the nearest tenth. 5 ft 10 ft 15 ft The area of the room is 188.3 ft 2.A = 25 + 75 + 88.3 = 188.3 ft 2 Area of the room:

41. Example 8-1a Find the area of the figure to the nearest tenth. Explore You know the dimensions of the figure. You need to find its area. Plan Solve a simpler problem. First, separate the figure into a triangle, square, and a quarter-circle. Then find the sum of the areas of the figure. Find Area of Irregular Figures

42. Example 8-1a Find the area of the figure to the nearest tenth. Solve Area of Triangle Area of a triangle Replace b with 2 and h with 4. Simplify.

43. Example 8-1a Find the area of the figure to the nearest tenth. Solve Area of Square Area of a square Replace b and h with 2. Simplify.

44. Example 8-1a Find the area of the figure to the nearest tenth. Solve Area of Quarter-circle Area of a quarter-circle Replace r with 2. Simplify. Answer: The area of the figure is or about 11.1 square inches.

45. Example 3-1a Find the area of the complex figure. The figure can be separated into a rectangle and two congruent triangles. Find the Area of a Complex Figure

46. Example 3-1b Area of rectangle Area of one triangle 5 Answer: The area of the figure is square inches.

47. Example 3-1c Find the area of the complex figure. Answer:

48. Example 3-2a Find the area of the complex figure. Round to the nearest tenth. The figure can be separated into two semicircles and a rectangle. Find the Area of a Complex Figure

49. Example 3-2b Area of one semicircle Area of rectangle Answer: The area of the figure is about square centimeters.

50. Example 3-2c Find the area of the complex figure. Round to the nearest tenth. Answer:

51. A school is creating a triangular playground. Find the area of the playground if the base is 80 yd and the height is 40 yd. The area is 1,600 yd 2. LESSON 6-4 = 1,600 Simplify. = (80)(40) Substitute. 1212 A = bh Use the area formula. 1212 Perimeter and Area of a Triangle Additional Examples

53. One method of estimating the area of an irregular figure is to count the number of squares the figure covers.

54. Additional Example 1: Finding Area by Counting Find the area of each figure. A. Count the full squares: 10 Count the half-full squares: 4 Add the number of full squares plus half the number of half-full squares: 10 + ( 4) = 10 + 2 =12 1212 The area of the figure is 12 square units.

55. For shapes such as the one in Example 1B you can only estimate the area. Helpful Hint

56. Additional Example 1: Finding Area by Counting Find the area of each figure. B. Count the full and almost-full squares: 11 Count the half-full squares: 4 Add the number of full squares plus half the number of half-full squares: 11 + ( 4) = 11 + 2 =13 1212 The area of the figure is approximately 13 square units.

57. Count the full squares: 11 Count the half-full squares: 8 Add the number of full squares plus half the number of half-full squares: 11 + ( 8) = 11 + 4 = 15 1212 The area of the figure is 15 square units. Partner Share! Example 1 Find the area of each figure. A.

58. Partner Share! Example 1 Find the area of each figure. B. Count the full and almost-full squares: 11 Count the half-full squares: 6 Add the number of full squares plus half the number of half-full squares: 11 + ( 6) = 11 + 3 =14 1212 The area of the figure is about 14 square units.

59. Additional Example 2A: Estimating Area Using Composite Figures Use a composite figure to estimate the shaded area. Draw a composite figure that approximates the irregular shape. Divide the composite figure into simple shapes.

60. area of the trapezoid: Additional Example 2A Continued Use a composite figure to estimate the shaded area. area of the triangle: A = bh 1 2 __ = (4 2) = 4 1 2 __ The shaded area is approximately 7 square units. A = h( b 1 + b 2 ) 1212 = 1(4 + 2) = 3 1212

61. Additional Example 2B: Estimating Area Using Composite Figures Use a composite figure to estimate the shaded area. Draw a composite figure that approximates the irregular shape. Divide the composite figure into simple shapes.

62. A = bh = 1 4 = 4 area of the rectangle: Additional Example 2B Continued Use a composite figure to estimate the shaded area. area of the semicircle: A = r 2 1 2 __  3.14(2 2 )  6.28 1 2 __ The shaded area is approximately 10.3 square units.

63. Draw a composite figure that approximates the irregular shape. Divide the composite figure into simple shapes. Partner Share! Example 2A Use a composite figure to estimate the shaded area.

64. A = bh = 3 2 = 6 area of the rectangle: Partner Share! Example 2A Continued Use a composite figure to estimate the shaded area. area of the triangle: A = bh 1 2 __ = (3 2) = 3 1 2 __ The shaded area is approximately 9 square units.

65. Partner Share! Example 2B Use a composite figure to estimate the shaded area. Draw a composite figure that approximates the irregular shape. Divide the composite figure into simple shapes.

66. A = s 2 = 2 2 = 4 area of the square: Partner Share! Example 2B Continued Use a composite figure to estimate the shaded area. area of the semicircle: A = r 2 1 2 __  3.14(1 2 )  1.57 1 2 __ The shaded area is approximately 5.5 square units.