Multi-Part Lesson 9-3 PART Composite Figures A Main Idea Find the perimeter of a composite figure. New Vocabulary perimeter composite figure glencoe.com B C D Perimeter of Composite Figures MOVIE THEATERS One of the largest movie theater screens is in St. Louis, Missouri. The 500-seat theater houses a 60-foot by 80-foot movie screen that is nearly twice the size of a traditional movie theater screen. 1. Suppose the theater owners wanted to put a fabric border around the screen. What would be the length of fabric? 280 ft 2. How did you find the distance around the screen? 3. How could you use multiplication and addition to find the distance around the screen? Sample answer: Multiply the length by 2 and width by 2. Add the products. Perimeter is the distance around a figure. Recall that a rectangle is a four-sided figure with four right angles and the opposite sides have equal lengths. 2. Sample answer: I added the length of each side. Perimeter of Rectangles Words Symbols Model The perimeter P of a rectangle is twice the sum of the base b and height h. h b P=b+b+h+h P = 2b + 2h or 2(b + h) C09-070A-891639 Find Perimeter of a Rectangle Find the perimeter of the rectangle. P = 2b + 2h Perimeter of a rectangle P = 2(7) + 2(13) Replace b with 7 and h with 13. P = 14 + 26 or 40 Multiply. Then add. The perimeter is 40 yards. 13 yd 7 yd C09-071A-891639 a. Find the perimeter of a rectangle with a base of 7.6 centimeters and a height of 4.9 centimeters. 25 cm 512 Chapter 9 Use Formulas in Geometry 512_516 SE.indd 512 7/9/09 4:34:05 PM Composite Figures Composite figures are also sometimes called complex figures or irregular figures. A composite figure is made of triangles, quadrilaterals, semicircles, and other two-dimensional figures. semicircle trapezoid To find the perimeter of a composite figure, add the distances around the closed figure. C09-072A-891639 Find Perimeter of a Composite Figure Find the perimeter of the figure. 4m 1.2 m 1m Add all of the distances around the composite figure. 1.2 m 4m P = 1.2 + 1.2 + 4 + 1 + 4 Sum of all sides P = 11.4 m Add. C09-074A-891639 The perimeter is 11.4 meters. Find the perimeter of each figure. b. 10.5 ft 5.5 ft 5.5 ft 5.5 ft 5.5 ft 43 ft c. 5 cm 5 cm 6 cm 10.5 ft 28 cm 6 cm 6 cm C09-075A-891639 GARDEN Find the perimeter of the garden to the nearest tenth. The distance around the semicircle is unknown. So, you need to find the circumference of a circle. C09-076A-891639 20 ft x 12 ft 8 ft 15 ft 25 ft semicircle Step 1 Find the circumference of the circle. C = πd Circumference of a circle C09-077A-891639 C = 3.14(15) Replace d with 15. Use 3.14 for π. C ≈ 47.1 Multiply. Step 2 Since you only need half of the circumference, divide by 2. The distance around the semicircle is approximately 47.1 ÷ 2 or 23.6. Step 3 Find the perimeter of the garden. The perimeter of the garden is 20 + 12 + 8 + 25 + 23.6 or 88.6 feet. Lesson 9-3 Composite Figures 512_516 SE.indd 513 513 7/9/09 4:34:07 PM 18 ft d. POOLS Find the perimeter of the pool shown. 73.68 ft 12 ft 12 ft 18 ft Find Missing Measures to Find C09-078A-891639 Perimeter Find the perimeter of the figure. 45 ft Find the unknown lengths by breaking the figure into two shapes. 40 ft 45 ft 15 ft ? 40 ft 35 ft ? 15 ft 5 ft 15 ft 30 ft 5 ft The sum must be 40 feet. 5 ft C09-079A-891639 The sum must be 45 feet. So, the perimeter is 45 + 40 + 15 + 5 + 30 + 35 or 170 feet. C09-080A-891639 56 cm f. 5.2 mm 16 cm e. 7 cm 12 cm 3.7 mm 3.1 mm 6.1 mm 8 cm C09-081A-891639 Examples 1 and 4 (pp. 512, 514) 19.6 mm C09-082A-891639 Find the perimeter of each figure. 1 2. 18 yd 2.9 cm 5 yd 46 yd 3. 12.6 cm 31 cm 18 m 20 m 88 m 11 m 24 m Examples 2 and 3 (p. 513) C09-084A-891639 4. FLAGS The flag of Ohio is the only state C09-083A-891639 flag that is not in the shape of a rectangle. Find the perimeter of the flag. 16 f 3 ft 5 ft 1.5 ft C09-086A-891639 1.5 ft 5 ft 514 Chapter 9 Use Formulas in Geometry $" 512_516 SE.indd 514 7/9/09 4:34:09 PM = Step-by-Step Solutions begin on page R1. Extra Practice begins on page EP2. Examples 1 and 2 (pp. 512–513) Find the perimeter of each figure. Use 3.14 for π. 5. 164 yd 40 yd 6. 21 yd 21 yd 21 yd 1.5 m 2m 21 yd 7. 2m 2m 40 yd 2m 1.5 m 62.27 cm 17 cm 8. 14 m 1.5 m 1.5 m 67.68 in. 15 in. C09-087A-891639 14 cm 14 cm 12 in. C09-089A-891639 11 cm 15 in. Example 3 (p. 513) 9. CARPENTRY Mr. Thomas wants to put a 5 ft 4 ft baseboard in the room shown. Find the C09-088A-891639 perimeter of the room to determine how C09-090A-891639 many feet of baseboard he will need. 64 ft 10 ft 15 ft 12 ft 18 ft 10. NASCAR One of the shortest professional racetracks is the Bristol Motor Speedway in Tennessee. Find the length, in feet, of one lap of the track. 3,121.2 ft Example 4 (p. 514) Find the perimeter of each figure. 11. 12 yd 15 yd 106 yd 12. $" 46.8 m 13 m 7.8 m 19 yd 17 yd 30 yd B 4 yd 650 ft $" ft 580 4.3 m 3.1 m 2.6 m 13 BASKETBALL A basketball court measures 26 meters by 14 meters. Ten meters of seating is added to each side of the court. Find the perimeter ofC09-093A-891639 the rectangle enclosed by the court and the seating area. 160 m C09-094A-891639 14. ALGEBRA Find the value of y given the perimeter P. How many segments y units long are needed for the perimeter? y = 9 cm; 6 segments P = 54 cm y y y Lesson 9-3 Composite Figures 515 C09-095A-891639 512_516 SE.indd 515 7/9/09 4:34:11 PM C 15. OPEN ENDED Draw and label a composite figure made up of a rectangle and semicircle with a perimeter between 100 and 200 centimeters. Find the perimeter. 16. CHALLENGE Find the perimeter of the figure at the right. 17. Describe how to find the distance around a semicircle. Practice 18. 8 in. 16 in. GRIDDED RESPONSE Mao is framing a picture. The picture frame is shown. What is the perimeter of the outside of the picture frame in inches? 10 in. 8 in. 16 in. C09-096A-891639 19. Phillipe draws an equilateral triangle. Next he draws a regular pentagon with the same perimeter as the triangle. How long is each side of the regular pentagon? 1 1 2 in. 6.4 in. 6.4 in. 6.4 in. 8 in. A. 32 in. C. 6.4 in. B. 25.6 in. D. 3.84 in. C09-098A-891639 $" _ Find the area of each circle. Use 3.14 or 22 for π. Round to the nearest tenth if 7 necessary. (Lesson 9-2D) 20. 21. 19 yd 22. 47 ft 7 11 in. 23. TRACK AND FIELD The diameter of the circle that a shot-putter stands in is 22 7 feet. What is the circumference of the circle? Use _ for π. (Lesson 9-2B) 7 C09-099A-891639 C09-100A-891639 C09-101A-891639 24. POPULATION As the fastest growing county in the U.S., the population of Flagler County, Florida, grew 10.7% in a recent year. Write 10.7% as a decimal. (Lesson 5-2D) 25. TRAVEL While working in a toll booth, Russ recorded the number of cars that had one passenger. Create a line plot of the data. (Lesson 3-2D) 516 Number of Cars with One Passenger 32 45 34 41 39 36 34 40 39 33 Chapter 9 Use Formulas in Geometry 512_516 SE.indd 516 7/10/09 9:39:27 AM

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