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# The figure above represents a semicircular garden that is enclosed by

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Math Expert
Joined: 02 Sep 2009
Posts: 60515
The figure above represents a semicircular garden that is enclosed by  [#permalink]

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09 Dec 2019, 03:11
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:16) correct 41% (01:43) wrong based on 35 sessions

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

Attachment:

1.jpg [ 23.49 KiB | Viewed 375 times ]

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Joined: 16 Feb 2015
Posts: 252
Location: United States
Concentration: Finance, Operations
Re: The figure above represents a semicircular garden that is enclosed by  [#permalink]

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09 Dec 2019, 03:36
1
Bunuel wrote:

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

Attachment:
1.jpg

Explanation:
2πr/2=20
r=20/π

Area of Semi-circle= (πr^2)/2= π{(20/π)^2}/2
= 200/π
IMO-D
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Joined: 27 Jul 2018
Posts: 20
Re: The figure above represents a semicircular garden that is enclosed by  [#permalink]

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09 Dec 2019, 22:43
Circumference = 2πr

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

Therefore:
2πr=40
=> πr=40/2
=> πr=20
=> r=20/π

Area of the garden
(πr^2)/2

= (π (20/π) (20/π))/2 = (400/π)/2 = 200/π Option D
Re: The figure above represents a semicircular garden that is enclosed by   [#permalink] 09 Dec 2019, 22:43
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