Question 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 $ABCD?$