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In the figure below, ABCD is a rectangle, and BE and CF are

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In the figure below, ABCD is a rectangle, and BE and CF are [#permalink] New post 01 Feb 2019, 11:41
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In the figure below, ABCD is a rectangle, and BE and CF are arcs of circles centered at A and D. What is the area of the striped region?

Attachment:
#GREpracticequestion In the figure below, ABCD.jpg
#GREpracticequestion In the figure below, ABCD.jpg [ 16.32 KiB | Viewed 237 times ]


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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Re: In the figure below, ABCD is a rectangle, and BE and CF are [#permalink] New post 02 Feb 2019, 06:39
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Carcass wrote:
In the figure below, ABCD is a rectangle, and BE and CF are arcs of circles centered at A and D. What is the area of the striped region?

Attachment:
#GREpracticequestion In the figure below, ABCD.jpg


A) \(10 - \pi\)

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

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

D) \(6 + 2\pi\)

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


Explanation::

The area of the rectangle = 5 * 2 = 10

Now for the arc area;

\(\frac{{Arc Area}}{{Circle Area}} = \frac{90}{360}\)

or Arc area =\(\frac{90}{360} * \pi * {radius}^2\)( radius of the circle = 2)

or Arc area = \(\pi\)

Since there are 2 Arc and both have the same radius ,

Therefore the area covered by the 2 Arc = \(2\pi\)

Therefore the Area of the shaded region = \(10 - 2\pi = 2(5 - \pi)\)
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Re: In the figure below, ABCD is a rectangle, and BE and CF are   [#permalink] 02 Feb 2019, 06:39
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In the figure below, ABCD is a rectangle, and BE and CF are

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