Let A B C D be a square. Let E, F, G, and H be the centers, respectively, of equilateral triangles with bases \overline{A B}, \overline{B C}, \overline{C D}, and \overline{D A}, each exterior to the square. What is the ratio of the area of square E F G H to the area of square A B C D ?
Answer Choices
A. 1
B. \dfrac{2+\sqrt{3}}{3}
C. \sqrt{2}
D. \dfrac{\sqrt{2}+\sqrt{3}}{2}
E. \sqrt{3}