1. Holt CA Course 1 9-5 Area of Composite Figures MG2.2 Estimate and compute the area of more complex or irregular two-and three- dimensional figures by breaking the figures down into more basic geometric objects. California Standards

2. Holt CA Course 1 9-5 Area of Composite Figures Additional Example 1A: Finding the Area of Composite Figures by Adding Find the shaded 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

3. Holt CA Course 1 9-5 Area of Composite Figures Additional Example 1A Continued Find the shaded 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

4. Holt CA Course 1 9-5 Area of Composite Figures 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.

5. Holt CA Course 1 9-5 Area of Composite Figures 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.

6. Holt CA Course 1 9-5 Area of Composite Figures A = bh A = 8 9 A = 72 yd 2 area of the rectangle: Check It Out! 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

7. Holt CA Course 1 9-5 Area of Composite Figures Check It Out! 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

8. Holt CA Course 1 9-5 Area of Composite Figures Check It Out! 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

9. Holt CA Course 1 9-5 Area of Composite Figures 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 Check It Out! 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

10. Holt CA Course 1 9-5 Area of Composite Figures 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

11. Holt CA Course 1 9-5 Area of Composite Figures Check It Out! 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.

12. Holt CA Course 1 9-5 Area of Composite Figures 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

13. Holt CA Course 1 9-5 Area of Composite Figures 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

14. Holt CA Course 1 9-5 Area of Composite Figures 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:

15. Holt CA Course 1 9-5 Area of Composite Figures Check It Out! 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

16. Holt CA Course 1 9-5 Area of Composite Figures Check It Out! 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

17. Holt CA Course 1 9-5 Area of Composite Figures Check It Out! 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: