GRE Geometry -- Overlapping Circles with an enclosed figure.

Question

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.

Answer 1

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 $h^2 + (r/2)^2 = r^2$.

Answer 2

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.