HKD1710 wrote:
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) \(1,200 + 150π\)
Please refer the enclosed diagram,
Area of the lot and driveway(EXCLUDING the shaded region)=Total area of the lot and driveway- Area of the shaded region(or shaded semicircle)
=(Area of the rectangle of size 30x40 +Area of the bigger semicircle with radius 20m)- Area of the shaded semi-circle with radius 10m
\(=30*40+\frac{1}{2}*\pi*20^2-\frac{1}{2}*\pi*10^2\)
=\(1200+\frac{1}{2}*\pi*(20^2-10^2)\)
=\(1200 + 150π\) sq. meter
Attachments
driveway.JPG [ 33.82 KiB | Viewed 944 times ]
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Regards,
PKN
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