AMC 8 2008 Problem 23

In square $ABCE$, $AF=2FE$ and $CD=2DE$. What is the ratio of the area of $\triangle BFD$ to the area of square $ABCE$?

$\textbf{(A)}\ \frac{1}{6} \textbf{(B)}\ \frac{2}{9} \textbf{(C)}\ \frac{5}{18} \textbf{(D)}\ \frac{1}{3} \textbf{(E)}\ \frac{7}{20}$