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The figure above represents a rectangular parking lot that is 30 meter

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HKD1710
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The figure above represents a rectangular parking lot that is 30 meter [#permalink] New post   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) \(1,200 + 150π\)

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Re: The figure above represents a rectangular parking lot that is 30 meter [#permalink] New post   18 Dec 2018, 21:13
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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
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Re: The figure above represents a rectangular parking lot that is 30 meter [#permalink] New post   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

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Re: The figure above represents a rectangular parking lot that is 30 meter [#permalink] New post   12 Feb 2019, 08:12
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) \(1,200 + 150π\)

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Attachment:
driveway.JPG


We can calculate the area by

Area of driveway = 1200

Area of not shaded semicircle = 200π

Area of shaded semicircle = 50π

Total area = 1200 +π (200 -50)
\(1,200 + 150π\)
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The figure above represents a rectangular parking lot that is 30 meter [#permalink] New post   05 Jan 2023, 23:21
Outer radius 20m
Hence, area is π20^2 = 400π
Since it is a half circle,
400π/2= 200π
Again,
Innner radius is 10m
Hence, area is π10^2= π100 or 50π
Now, the area of driveway except the shaaded region is 200π-50π= 150π

The answer is 1200+150π

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The figure above represents a rectangular parking lot that is 30 meter [#permalink]
05 Jan 2023, 23:21
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