Find the area of the shaded region in the figure. (Round your answer to one decimal place.)
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2 Answers
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Area of Triangle
The central angle is π/3 therefor this is an equilateral triangle
The height of an equilateral triangle is always (√3)/2 * side
h = (√3)* 17/2
a = bh/2
a = 17 ( (√3) 17/2 ) / 2
a = (289/4)√3
a ≈ 125.140670846851384
Area of sector
a = (ø/2)r²
a = ( (π/3) / 2) * 17²
a = (π/6) 289
a ≈ 151.320046147908374
Area of circle
a = πr²
a = π (17²)
a = 289π
a ≈ 907.920276887450246
Area of shaded region
a = area of circle – area of sector + area of triangle
a ≈ 907.920276887450246 – 151.320046147908374 + 125.140670846851384
a ≈ 881.7409015864
a ≈ 881.7 units² <–––––––
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Ok
