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- 1. 1.7 Notes Perimeter, Circumference, Area.
- 2. 1.7 Notes Perimeter, Circumference, Area. Perimeter & circumference are measured in units of length (inches, feet, yards, miles, meters, kilometers, centimeters, etc). Area is measured in “square units,” using the following notation: “square feet” – ft2, “square inches” – in2, “square meters” m2, etc.† In a circle, the radius is ½ of the diameter, and the diameter is 2 times as long as the radius (r = d/2 or d =2r) For π, use either 3.14 or the button on the calculator (3.141592654…) †Ask Dr. Math for a discussion on “square units” vs. “units squared.”
- 3. EXAMPLE 1 Find the perimeter and area of a rectangle Basketball Find the perimeter and area of the rectangular basketball court shown. SOLUTION Perimeter P = 2l + 2w = 2(84) + 2(50) = 268 ANSWER Area A = lw = 84(50) = 4200 The perimeter is 268 feet and the area is 4200 square feet.
- 4. EXAMPLE 2 Find the circumference and area of a circle Team Patch You are ordering circular cloth patches for your soccer team’s uniforms. Find the approximate circumference and area of the patch shown. SOLUTION First find the radius. The diameter is 9 centimeters, so the radius is 1 (9) = 4.5 centimeters. 2 Then find the circumference and area. Use 3.14 to approximate the value of π.
- 5. EXAMPLE 2 Find the circumference and area of a circle C = 2πr 2(3.14) (4.5) = 28.26 A = πr 2 3.14(4.5) = 63.585 ANSWER The circumference is about 28.3 cm2. The area is about 63.6 cm . 2
- 6. GUIDED PRACTICE for Examples 1 and 2 Find the area and perimeter (or circumference) of the figure. If necessary, round to the nearest tenth. ANSWER 74.1 m2, 37.4 m
- 7. GUIDED PRACTICE for Examples 1 and 2 Find the area and perimeter (or circumference) of the figure. If necessary, round to the nearest tenth. ANSWER 2.6 cm2, 6.4 cm
- 8. GUIDED PRACTICE for Examples 1 and 2 Find the area and perimeter (or circumference) of the figure. If necessary, round to the nearest tenth. ANSWER 12.6 yd2, 12.6 yd
- 9. EXAMPLE 3 Perimeter & Area in the coordinate plane What is the perimeter of triangle RQS? What is the area? Animated Solution Answers: perimeter 13.1 units; area = 8 square units.
- 10. EXAMPLE 4 Solve a multi-step problem Skating Rink An ice-resurfacing machine is used to smooth the surface of the ice at a skating rink. The machine can resurface about 270 square yards of ice in one minute. About how many minutes does it take the machine to resurface a rectangular skating rink that is 200 feet long and 90 feet wide? SOLUTION The machine can resurface the ice at a rate of 270 square yards per minute. So, the amount of time it takes to resurface the skating rink depends on its area.
- 11. EXAMPLE 4 STEP 1 Solve a multi-step problem Find the area of the rectangular skating rink. Area = lw = 200 (90) = 18,000 ft 2 The resurfacing rate is in square yards per minute. Rewrite the area of the rink in square yards. There are 3 feet in 1 yard, and 32 = 9 square feet in 1 square yard. 18,000 ft 2 1 yd 2 2000 yd 2 = 9 ft 2 Use unit analysis.
- 12. EXAMPLE 4 STEP 2 Solve a multi-step problem Write a verbal model to represent the situation. Then write and solve an equation based on the verbal model. Let t represent the total time (in minutes) needed to resurface the skating rink. 2000 = 270 t 7.4 t ANSWER Substitute. Divide each side by 270. It takes the ice-resurfacing machine about 7 minutes to resurface the skating rink.
- 13. GUIDED PRACTICE 4. for Examples 3 and 4 Describe how to find the height from F to EG in the triangle. ANSWER The height is the length of the segment from point F to EG at the point (1,3). Using the coordinate grid to count units , the height is 6.
- 14. GUIDED PRACTICE for Examples 3 and 4 5. Find the perimeter and the area of the triangle shown. ANSWER about 16.8, 12
- 15. GUIDED PRACTICE 6. for Examples 3 and 4 What if ? In Example 4, suppose the skating rink is twice as long and twice as wide. Will it take an ice-resurfacing machine twice as long to resurface the skating rink? Explain your reasoning. ANSWER No; the new area is more than twice as big.
- 16. EXAMPLE 5 Find unknown length The base of a triangle is 28 meters. Its area is 308 square meters. Find the height of the triangle. SOLUTION 1 bh = 2 308 = 1 (28) h 2 A 22 = h ANSWER Write formula for the area of a triangle. Substitute 308 for A and 28 for b. Solve for h. The height is 22 meters.
- 17. GUIDED PRACTICE for Example 5 7. The area of a triangle is 64 square meters, and its height is 16 meters. Find the length of its base. ANSWER 8 m.
- 18. EXAMPLE 3 Animated Solution!! Click for steps!! Perimeter: Use the ruler postulate to find the length of QS (since it is a horizontal segment). For RS and RQ, use the distance formula. Then add up all the side lengths to find the perimeter. QS = 5 – 1 = 4 units QR = (4 – 1)2+ (6 – 2)2 = 25 = 5 units RS = (5 – 4)2+ (2 – 6)2 = 17 4.1 units Then find the perimeter. P = QS + QR + RS 4 + 5 + 4.1 = 13.1 units
- 19. EXAMPLE 3 Animated Solution!! Click for steps!! Area: You know QS from the previous problem. To find the height, drop down from R to segment QS, and use the ruler postulate again. QS = 5 – 1 = 4 units (4, 2) h = 6 – 2 = 4 units Then find the area. A = 1/2 bh Back to Notes A = 1/2 (4)(4) A=8 The area is 8 square units.

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