Area of Composite Figures

9-6 Area of Composite Figures Find the area of the figure. Round to the nearest tenth if necessary. 1. SOLUTION: The figure can be separated into a trapezoid and a rectangle. Find the area of each. Area of Trapezoid The height is 8 – 4, or 4 inches. Area of the Rectangle The area of the figure is 26.6 + 32 or 58.6 square inches. ANSWER: Page 1 9-6 Area of Composite Figures 3. The floor plan of a kitchen is shown. If the entire kitchen floor is to be tiled, how many square feet of tile are needed? SOLUTION: The figure is a rectangle with a trapezoid section missing. Find the area of each. Subtract the area of the trapezoid from the area of the rectangle. Area of Trapezoid The unknown base is 16 – (6 + 6), or 4 feet. The height is 12 – 11, or 1 foot. Area of the Rectangle The square footage of tile needed is 192 – 3 or 189 square feet. ANSWER: Page 2 9-6 Area of Composite Figures 5. The diagram shows one side of a storage barn. a. This side needs to be painted. Find the total area to be painted. b. Each gallon of paint costs $20 and covers 350 square feet. Find the total cost to paint this side once. Justify your answer. SOLUTION: a. The side of the barn can be separated into a triangle and a rectangle. Find the area of each. Area of Rectangle Area of Triangle The height is 26.5 – 14.5, or 12 feet. The total area to be painted is 330.6 + 136.8 or 467.4 square feet. b. You will need 467.4 ÷ 350 ≈ 1.34 gallons of paint. Since only whole gallons of paint can be purchased, you will need 2 gallons of paint. At $20 each, the cost will be 2 × $20 or $40. ANSWER: a. b. 467.4 ÷ 350 ≈ 1.34; Since only whole gallons of paint can be purchased, you will need 2 gallons of paint. At $20 each, the cost will be 2 × $20 or $40. Page 3 9-6 Area of Composite Figures 7. Persevere with Problems Describe, how to separate the figure into simpler figures. Then estimate the area. One square unit equals 2,400 square miles. Justify your answer. SOLUTION: Sample answer: Add the areas of a rectangle and a triangle. Area of rectangle: 3 × 4 = 12; Area of triangle: ; 12 + 4.5 = 16.5. So, an approximate area is 16.5 × 2,400 or 39,600 square miles. ANSWER: Sample answer: Add the areas of a rectangle and a triangle. Area of rectangle: 3 × 4 = 12; Area of triangle: ; 12 + 4.5 = 16.5. So, an approximate area is 16.5 × 2,400 or . 9. Make a Conjecture Refer to the composite figure at the right. Make a conjecture about how the area of the composite figure changes if each dimension given is doubled. Then test your conjecture by doubling the dimensions and finding the area. SOLUTION: The area of the composite figure will be 4 times greater when the dimensions are doubled. The find area of the original figure by creating a triangle and rectangle within the figure. Area of triangle Page 4 9-6 Area of Composite Figures Area of the rectangle The total original area is 45.1 + 114.8 = 159.9 square cm Find the new area after doubling the dimensions. Area of triangle Area of the rectangle The total area of the new figure is 180.4 + 459.2 = 639.2 square cm To find how many times larger the new area is divide the new area by the original area. The new figure has an area that is 4 times greater than the original. ANSWER: The area is multiplied by 4. Original area: 159.9 square cm; new area: 639.6 square cm Page 5 9-6 Area of Composite Figures Find the area of the figure. Round to the nearest tenth if necessary. 11. SOLUTION: The figure can be separated into a square and a triangle. Find the area of each. Area of Square Area of Triangle The base is 4 + 5.2 + 2, or 11.2 yards. The area of the figure is 27.0 + 39.2 or 66.2 square yards. ANSWER: Page 6 9-6 Area of Composite Figures 13. At the local zoo, the aquarium can be seen from the Reptile Room and the Amphibian Arena. What is the total area of both rooms and the aquarium? SOLUTION: Area of Reptile Room: 72 × 83 or 5976 Area of Amphibian Arena: 72 × 83 or 5976 The sum of the areas: 5976 + 5976 or 11,952 Overlapping area: 20 × 51 or 1,020 Subtract the overlapping area: 11,952 – 1,020 = 10,932 square feet ANSWER: 10,932 ft2 Page 7 9-6 Area of Composite Figures 15. A window has the dimensions shown. Determine if each statement is true or false. a. The area of the trapezoid section of the window is 648 square inches. True False b. The area of the rectangular section of the window is 1,728 square inches. True False c. The area of the entire window is 2,376 square inches. True False SOLUTION: a. area of the trapezoid The area of the trapezoid is 324 square inches, so letter a is false. b. area of rectangle The area of the rectangle is 1,728 square inches. So letter b is true. c. The area of the window is 1,728 + 324 or 2,052 square inches. So letter c is false. ANSWER: a. false b. true c. false Page 8 9-6 Area of Composite Figures Multiply. 17. 36 × 12 = SOLUTION: ANSWER: 432 19. 72 × 200 = SOLUTION: ANSWER: 14,400 21. Hiking burns about 144 Calories each half hour. About how many Calories can be burned if someone hikes 3 days a week for an hour? SOLUTION: Since 144 Calories are burned each half hour, 144 + 144 or 288 Calories are burned in an hour. So, for 3 days a person can burn 288 × 3 or 864 Calories. ANSWER: 864 Calories Page 9