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Each of the triangles is equilateral.

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Director
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Each of the triangles is equilateral. [#permalink] New post 16 Aug 2018, 09:19
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Question Stats:

25% (00:42) correct 75% (01:40) wrong based on 12 sessions
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Each of the triangles is equilateral.

Quantity A
Quantity B
The area of the
shaded region
\(6\pi\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA
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Director
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Re: Each of the triangles is equilateral. [#permalink] New post 17 Aug 2018, 00:11
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amorphous wrote:
Each of the triangles is equilateral.

Quantity A
Quantity B
The area of the
shaded region


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.



Given the radius of the circle is 3 (since one side of the equilateral triangle is 3)

Now the area of the circle =\(\pi * radius^2 = \pi * 3^2 = 9\pi\)

Now we need to find the area of the sector covered by the 2 equilateral triangle,

\(\frac{{Sector Area}}{{circle area}} = \frac{{Central angle}}{360}\)

Sector area =\(\frac{60}{360} * circle area =\frac{60}{360} * 9\pi = \frac{{3\pi}}{2}\)

Since there are two sectors so the total sectors not covered in shaded area =\(\frac{{6\pi}}{2}\)

Therefore the area under the shaded area = circle area - area of the 2 sectors = \(9\pi - \frac{{6\pi}}{2}= \frac{{12\pi}}{2} = 6\pi\)

Hence both are equal, i.e. option C
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Re: Each of the triangles is equilateral.   [#permalink] 17 Aug 2018, 00:11
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Each of the triangles is equilateral.

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