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geometry

by oks » Sun May 31, 2009 11:08 am
The figure above represents a rectangular parking lot that is 30 meters by 40 meters and an attached semicircular driveway that has an outer radius of 20 meters and an inner radius of 10 meters. If the shaded region is not included, what is the area, in square meters, of the lot and driveway?
(A) 1,350π
(B) 1,200 + 400π
(C) 1,200 + 300π
(D) 1,200 + 200π
(E) 1,200 + 150π

OA is E, but why not B? What am I missing?

Thanks![/img]
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by raleigh » Sun May 31, 2009 11:18 am
Break up the area into area of the rectangle + area of the large semi circle - area of the small semi circle.

area of the rectangle is 40*30 = 1200

The area of a semi cricle is half the area of a circle of radius r so
area of the large semi cricle is pi*r^2/2 = pi*400/2 = 200pi
area of the small semi circle is pi*r^2/2 = pi*100/2 = 50pi

So we get 1200 + 200pi - 50pi = 1200 + 150pi
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