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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] New post 07 Sep 2014, 06:22
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80% (00:46) correct 19% (01:14) wrong based on 21 sessions
Attachment:
figure 9.jpg
figure 9.jpg [ 12.76 KiB | Viewed 1664 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] New post 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).

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

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