SOLUTION: Draw a isosceles triangle ACB which is inscribed in a semicircle with a diameter of length 32.Find the area of the shaded region in terms of pie.(the shaded region is the circle)

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Question 199256: Draw a isosceles triangle ACB which is inscribed in a semicircle with a diameter of length 32.Find the area of the shaded region in terms of pie.(the shaded region is the circle)
Answer by RAY100(1637) (Show Source):
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Remember that a triangle inscribed in a semicircle is a rt triangle,,,,therefore we have a rt isosceles triangle ,,,with hypotenuse = 32.
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since the ratio of sides are 1 :1:sqrt2 ,,,, 32 / sqrt2 = s / 1,,, or s= 22.627,,,(16 sqrt2)
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Area of triangle = 1/2 *b *h = 1/2 * 22.627 *22.627 = 256
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Area of semi circle = 1/2 * pi * r^2 = 1/2 * pi * 16^2 = 128 * pi
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Area of shaded area between is ( 128 pi - 256) = 128 (pi-2)