+1678 Four equilateral triangles, $\triangle{ABG}$, $\triangle{BCH}$, $\triangle{CDE}$ and $\triangle{DAF}$, are constructed inside square $ABCD,$ as shown. Points $E, F, G$ and $H$ are the vertices of the triangles that lie within square $ABCD.$ What is the ratio of the area of triangle $ABE to the area of square $ABCD$? Express your answer in simplest radical form.
