2016 AMC 12A Problem 17

Let ABCD be a square. Let E, F, G and H be the centers, respectively, of equilateral triangles with bases \overline{AB}, \overline{BC}, \overline{CD}, and \overline{DA}, each exterior to the square. What is the ratio of the area of square EFGH to the area of square ABCD?

\textbf{(A)}\ 1\qquad\textbf{(B)}\ \frac{2+\sqrt{3}}{3} \qquad\textbf{(C)}\ \sqrt{2} \qquad\textbf{(D)}\ \frac{\sqrt{2}+\sqrt{3}}{2} \qquad\textbf{(E)}\ \sqrt{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.