What is the perimeter of the shaded region?

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What is the perimeter of the shaded region?

by AAPL » Sat Jun 02, 2018 5:51 am

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A

B

C

D

E

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In the figure above, AB is the diameter of a circle of radius 6, what is the perimeter of the shaded region?

$$A.\ \pi+6+6\sqrt{3}$$
$$B.\ \pi+12+6\sqrt{3}$$
$$C.\ 2\pi+9+6\sqrt{3}$$
$$D.\ 2\pi+12+6\sqrt{3}$$
$$E.\ 2\pi+12+12\sqrt{3}$$

The OA is D.

What I don't understand about this problem- why wouldn't it work if we tried to use 30 degrees to calculate the arc length? Using that I arrived at answer B.

Is there a strategic approach to solve this PS question? Can anyone help? Thanks!
Source: — Problem Solving |