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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]  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 [ 16.32 KiB | Viewed 224 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]  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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