12-3 Area of Composite Figures
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1 Find the area of each figure. Round to the nearest tenth, if necessary The Jamesons hired a landscaper to brick their walkway. One case of bricks costs $25 and covers 6 square feet cm 2 a. What is the area of the walkway? b. How many cases are needed to cover the walkway with bricks? What would be the cost? a. 58 ft 2 b. 10 cases; $250 Find the area of each figure. Round to the nearest tenth, if necessary in m cm ft in 2 esolutions Manual - Powered by Cognero Page 1
2 ft ft Refer to the swimming pool shown mm 2 a. What is the area of the pool s floor? b. A pool cover costs $1.70 per square foot. How much would a cover for the pool cost? a ft 2 b. $ in 2 esolutions Manual - Powered by Cognero Page 2
3 13. Financial Literacy Mr. Reyes wants to carpet his family room. 17. Find the area of the part of the shuffleboard court shown. a. What is the area of the space to be carpeted? b. If carpet costs $2.25 per square foot, how much would it cost to carpet Mr. Reyes family room if there is no leftover carpet? a. 354 ft 2 b. $ ft A diagram of the Denali National Park Wilderness area in Alaska is shown. 14. What is the area of a figure that is formed using a rectangle 10 feet long and 7 feet wide and a semicircle with a diameter of 7 feet? 89.2 ft A figure is formed using a semicircle and a triangle that has a base of 8 inches and a height of 12 inches. Find the area of each figure to the nearest tenth. a. The diameter of the semicircle equals the base of the triangle. b. The diameter of the semicircle equals the height of the triangle. a in 2 b in 2 a. Describe how the irregular shape can be separated into polygons to find its area. b. Estimate the number of square miles contained in the Denali National Park Wilderness area. c. Estimate the perimeter of the Wilderness area. a. It can be separated into two trapezoids. b mi 2 c. Sample answer: 271 mi 16. A rectangular room is 15 feet long and 12 feet wide. It has a semicircle on each 12-foot side. What is the area of the room? Round to the nearest tenth ft 2 esolutions Manual - Powered by Cognero Page 3
4 Find the area of each shaded region. Round to the nearest tenth, if necessary Multiple Representations In this problem, you will investigate areas of composite figures m 2 a. Words Describe the figure using names of geometric figures whose areas you can find. b. Symbols List the formulas that you can use to find the area of the composite figure. c. Analyze 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. a. rectangle, triangle ft in 2 b. A = lw, A = bh c. The area is multiplied by 4. Original area: cm 2 ; New area: cm Model with Mathematics Describe real-life composite figures whose areas can be found by separating the figures into geometric figures that have area formulas. Sample answer: states, parks, shopping malls 24. Persevere with Problems Reena created the flower shown by placing semicircles around a regular pentagon. Using the measurements shown, find the area of the flower. Round to the nearest tenth in 2 esolutions Manual - Powered by Cognero Page 4
5 25. Reason Abstractly Suppose a playground is in the shape of a composite figure that has a curved side that is not a semicircle. Describe how you could estimate the area of the playground. 28. Find the area of the shaded region. Use 3.14 for π. Round to the nearest hundredth. Sample answer: Use polygons to approximate the shape of the curved side of the playground. 26. Building on the Essential Question Describe how circles and polygons help you find the area of a composite figure. Give an example by drawing and labeling a composite figure. Describe the figures that can be used to find the area and then find the area. Sample answer: You can use polygons and circles to find the area of a composite figure by finding the area of each individual figure and then adding the areas. A ft 2 B ft 2 C ft 2 D ft 2 C 29. The Lin family is buying a cover for their swimming pool shown. The cover costs $3.19 per square foot. How much will the cover cost? semicircle and rectangle; about 34.3 in Short Response In the diagram, a patio that is 4 feet wide surrounds a swimming pool. What is the area of the patio in square feet? Round to the nearest tenth. F $ G $ H $ J $ ft 2 J esolutions Manual - Powered by Cognero Page 5
6 30. Find the difference between the areas of the two bedrooms (not including the closet). A 27 ft 2 B 40 ft 2 C 58 ft 2 D 168 ft 2 B Find the circumference and area of each circle. Round to the nearest tenth. 31. radius 6 centimeters 37.7 cm; cm diameter 14 inches 44.0 in.; in diameter feet 29.8 ft; 70.9 ft radius 9 feet 56.5 ft; ft diameter 8 millimeters 25.1 mm; 50.3 mm 2 Find the area of each figure described. 37. triangle: base, 9 inches; height, 6 inches 27 in trapezoid: height, 3 centimeters; bases, 4 centimeters, 8 centimeters 18 cm Jeremy can run miles in 25 minutes. How many minutes would it take him to run 5 miles at this same rate? 37 min 30 s Find the percent of change. 40. The cost of a monthly pass for students on the Baxterville Bus Line increased from $30 to $33. What was the percent increase in the cost? 10% 41. Membership in the school orchestra fell from 120 members to 102 members this year. What was the percent decrease in membership? 15% 35. radius 20 in in.; in 2 esolutions Manual - Powered by Cognero Page 6
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