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# The figure above represents a semicircular garden that is en

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The figure above represents a semicircular garden that is en [#permalink]  06 Dec 2019, 02:15
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34% (00:53) correct 65% (00:55) wrong based on 29 sessions
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#greprepclub The figure above represents a semicircular garden.jpg [ 23.49 KiB | Viewed 702 times ]

The figure above represents a semicircular garden that is enclosed by 20 feet of fencing and a straight garden wall. What is the area, in square feet, of the garden?

A. $$\frac{20}{\pi}$$

B. $$\frac{50}{\pi}$$

C. $$\frac{100}{\pi}$$

D. $$\frac{200}{\pi}$$

E. $$\frac{400}{\pi}$$

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[Reveal] Spoiler: OA

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Re: The figure above represents a semicircular garden that is en [#permalink]  09 Dec 2019, 00:56
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D. Double the circumference of the semi-circle. So that's 40 feet. Equate to the formula of circumference and solve for d. That's 40/π. Divide by 2 to get the radius 20/π. Apply the formula for area since you now know the radius. Note that this is for the whole circle, divide by 2 to get for the semicircle.
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Re: The figure above represents a semicircular garden that is en [#permalink]  14 Jun 2020, 05:26
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Re: The figure above represents a semicircular garden that is en [#permalink]  14 Jun 2020, 09:25
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Expert's post
Circumference = $$2πr$$

Half of circumference is 20. So full circumference is 40.

Therefore:

$$2πr=40$$

=> $$πr=\frac{40}{2}$$

=> $$πr=20$$

=> $$r=\frac{20}{π}$$

Area of the garden

$$\frac{(πr^2)}{2}$$

= $$\frac{(π (\frac{20}{π}) (\frac{20}{π}))}{2} = \frac{(\frac{400}{π})}{2} = \frac{200}{π}$$ Option D
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Re: The figure above represents a semicircular garden that is en   [#permalink] 14 Jun 2020, 09:25
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