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18 Dec 2018, 10:27
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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) \(1,200 + 150π\)
Attachment:
driveway.JPG [ 17.53 KiB | Viewed 15401 times ]
18 Dec 2018, 21:13
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HKD1710
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
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driveway.JPG [ 33.82 KiB | Viewed 14519 times ]
19 Dec 2018, 12:14
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Area of rectangle 40*30 = 1200
Area of smal semi circle = piR^2 / 2 = 10^2 / 2 = 50
Area of large semi circle = piR^2/2 = 20^2 / 2 = 200
Area of large semicircle - area of small semicircle = 200 -50 = 150
Area of the lot and driveway 1200+150p
E
Area of smal semi circle = piR^2 / 2 = 10^2 / 2 = 50
Area of large semi circle = piR^2/2 = 20^2 / 2 = 200
Area of large semicircle - area of small semicircle = 200 -50 = 150
Area of the lot and driveway 1200+150p
E
