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 interior to the square. What is the ratio of the area of square $EFGH$ to the area of square $ABCD$?