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Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).

Find the area of the shaded regions below. Give your answer as a completely simplified-example-1

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Answer: 8pi - 8sqrt(3) cm^2

Explanation:

The area of the shaded regions would be equal to the area of the semi circle minus the area of the triangle.

The area of the semi circle = the area of the circle/2

= 16pi/2

= 8 pi cm^2

By Thale's theorem, we can conclude triangle ABC is a right triangle with AB being the hypotenuse. It is a 30 60 90 triangle specifically.

Therefore, AC = 4 sqrt(3).

Thus, the area of the triangle = 4*4sqrt(3)/2

= 8 sqrt(3) cm^2

The area of the shaded regions = 8pi - 8sqrt(3) cm^2

User JakeTheSnake
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