AHSME 1991 Problem 23

If $ABCD$ is a $2\times2$ square, $E$ is the midpoint of $\overline{AB}$,$F$ is the midpoint of $\overline{BC}$,$\overline{AF}$ and $\overline{DE}$ intersect at $I$, and $\overline{BD}$ and $\overline{AF}$ intersect at $H$, then the area of quadrilateral $BEIH$ is $\text{(A) } \frac{1}{3} \text{(B) } \frac{2}{5} \text{(C) } \frac{7}{15} \text{(D) } \frac{8}{15} \text{(E) } \frac{3}{5}$