10.7 Areas of Circles and Sectors

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10.7 Areas of Circles and Sectors Learning Target: I can find the area of circles, sectors, and segments. 10.7 Areas of Circles and Sectors

Area of a Sector Sector of a Circle – region bounded by 2 radii and their intercepted arc

Ex. 1 Find the area of the sector. Leave in terms of . 360° = • r2 90° 360° = • (4)2 = 4  ft2

Ex. 2 Find the area of the sector. Leave in terms of . 360° = • r2 315° 360° = • (4)2 = 14 in2

Asegment = Asector - AΔ Area of a Segment Segment of a Circle – Part of a circle bounded by an arc & the segment joining its endpoints. Asegment = Asector - AΔ Area of a Δ A = ½ bh

Ex. 1: Find the area of the segment Ex.1: Find the area of the segment. Round your answer to the nearest tenth. C mABC = 90° 10cm Trianlge Area ½bh ½(10)(10) 50cm2 Sector Area = mARC 360 • r2 = 90 360 • (10)2 = 78.5 cm2 B 90 ° A Segment Area = Sector Area- Triangle Area = 78.5 – 50 = 28.5 cm2

Ex. 3: Find the area of the shaded region Ex.3: Find the area of the shaded region. (note: you will add the sector area to the triangle area) Round your answer to the nearest tenth. Trianlge Area ½bh ½(11)(11) 61cm2 Sector Area = mARC 360 • r2 = 270 360 • (11)2 = 284.955 cm2 Shaded Area = Sector Area + Triangle Area = 284.955 + 61 = 345.955cm2