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Hi I'm having trouble solving this problem from a quantitative reasoning question on the GRE. The diagram and the word problem are shown above. I think I'm lost as to the properties a parallelogram or triangles that would help me solve the above problem.

Thanks.

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2 Answers 2

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Shaded region is made up of two equal equilateral triangles, with sides equal r. The area of one triangle is $r^2\sqrt{3}/4$. Thus the correct answer is B.

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Shaded region is made up of two equal equilateral triangles, with sides equal $r$. The area of one triangle is $(1/2)r^2\sqrt{3}/2$. Thus the correct answer is $B$.

You can prove that the height, $h$, in the equilateral triangle is $h = r\sqrt{3}/2$ by observing that $h^2 + (r/2)^2 = r^2$.

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