SOLUTION: Find the area of the shaded region in the figure. (Round your answer to one decimal place.) USE LINK FOR PICTURE http://www.webassign.net/waplots/7/7/84eaf04fe7ca06731479a31a5

Question 1008994: Find the area of the shaded region in the figure. (Round your answer to one decimal place.)
USE LINK FOR PICTURE
http://www.webassign.net/waplots/7/7/84eaf04fe7ca06731479a31a56bf2e.gif
PLEASE HELP!!!
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Okay, the area of the shaded region is of course the area of the circle minus the area of the segment, as shown.
We can find the area of the circle as A = (pi)r^2 = 324(pi)
The segment can be found by subtracting the equilateral triangle of side 18 from 1/6 the area of the circle, so
A(segment) = (1/6)(pi*r^2) - s^2*sqrt(3) / 4
A(segment) = (1/6)(324pi) - 18^2*sqrt(3) / 4
A(segment) = 54(pi) - 81*sqrt(3)
And then the final shaded area is
A(shaded) = 324(pi) - [54(pi) - 81*sqrt(3)] = 270(pi) + 81*sqrt(3)
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