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Because the diameters are in different units, convert 1 ft to 12 in.

2 2. The radius of the archery target is = 1 ft. Because the diameters are in different units, convert 1 ft to 12 in. The radius of the archery target is 1 ft = 12 in. The area of the archery target is r 2 = (12) 2 = 144 in. 2. Areas of Circles and Sectors. LESSON 10-7.

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Because the diameters are in different units, convert 1 ft to 12 in.

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  1. 2 2 The radius of the archery target is = 1 ft. Because the diameters are in different units, convert 1 ft to 12 in. The radius of the archery target is 1 ft = 12 in. The area of the archery target is r2 = (12)2 = 144 in.2 Areas of Circles and Sectors LESSON 10-7 Additional Examples A circular archery target has a 2-ft diameter. It is yellow except for a red bull’s-eye at the center with a 6-in. diameter. Find the area of the yellow region. Round your answer to the nearest whole number. Find the areas of the archery target and the bull’s-eye.

  2. The area of the red region is r2 = (3)2 = 9 in.2 area of archery target – area of red region = area of yellow region 144 – 9 = 135 Use a calculator. 135 6 2 The radius of the red region is = 3 in. Areas of Circles and Sectors LESSON 10-7 Additional Examples (continued) The area of the yellow region is about 424 in.2 Quick Check

  3. Find the area of sector ACB. Leave your answer in terms of . mAB 360 area of sector ACB = • r2 100 360 = • (6)2 5 18 = • 36 = 10 The area of sector ACB is 10 m2. Areas of Circles and Sectors LESSON 10-7 Additional Examples . . Quick Check

  4. area of sector AOB = • r2Use the formula for area of a sector. mAB 360 120 360 = • (24)2Substitute. = • 576 = 192 Simplify. 1 3 Areas of Circles and Sectors LESSON 10-7 Additional Examples Find the area of the shaded segment. Round your answer to the nearest tenth. Step 1: Find the area of sector AOB.

  5. Step 2: Find the area of AOB. AOB has base 12 3 ft + 12 3 ft, or 24 3 ft and height 12 ft. 1 2 A = bh Area of a triangle A = (24 3 )(12) Substitute 24 for b and 12 for h. A = 144 3 Simplify. 1 2 Areas of Circles and Sectors LESSON 10-7 Additional Examples (continued) You can use a 30°-60°-90° triangle to find the height h of AOB and AB. 24 = 2hhypotenuse = 2 • shorter leg 12 = hDivide each side by 2. = 3 • 12 = 12 3 longer leg = 3 • shorter leg AB = 24 3 Multiply each side by 2. AB 2

  6. area of segment = 192 – 144 3 Use a calculator. Areas of Circles and Sectors LESSON 10-7 Additional Examples (continued) Step 3: Subtract the area of AOB from the area of sector AOB to find the area of the segment of the circle. To the nearest tenth, the area of the shaded segment is 353.8 ft2. Quick Check

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