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# GRE Math Challenge #11-ABCD is a rectangle, and BE and CF

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GRE Math Challenge #11-ABCD is a rectangle, and BE and CF [#permalink]  07 Sep 2014, 06:22
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Question Stats:

82% (00:48) correct 17% (01:14) wrong based on 23 sessions
Attachment:

figure 9.jpg [ 12.76 KiB | Viewed 1830 times ]

In the figure, ABCD is a rectangle, and BE and CF are arcs of circles centred at A and D. What is the area of the shaded region?

A. $$10 - \pi$$

B. $$2(5 - \pi)$$

C. $$2(5 -2\pi)$$

D. $$6 + 2\pi$$

E. $$5(2 - \pi)$$
[Reveal] Spoiler: OA

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Last edited by Carcass on 29 Nov 2017, 12:33, edited 1 time in total.
Edited by Carcass
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Re: GRE Math Challenge #11-ABCD is a rectangle, and BE and CF [#permalink]  23 Jul 2018, 17:34
Expert's post
sandy wrote:
Attachment:
figure 9.jpg

In the figure, ABCD is a rectangle, and BE and CF are arcs of circles centred at A and D. What is the area of the shaded region?

A. $$10 - \pi$$

B. $$2(5 - \pi)$$

C. $$2(5 -2\pi)$$

D. $$6 + 2\pi$$

E. $$5(2 - \pi)$$

The area of the rectangle is 5 x 2 = 10. The total area of the two quarter-circles is 2 x (¼ x π x 2^2) = 2π. Therefore, the area of the shaded region is 10 - 2π = 2(5 - π).

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Re: GRE Math Challenge #11-ABCD is a rectangle, and BE and CF   [#permalink] 23 Jul 2018, 17:34
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