2012 AMC 10B Problem 19

In rectangle ABCD, AB=6, AD=30, and G is the midpoint of \overline{AD}. Segment AB is extended 2 units beyond B to point E, and F is the intersection of \overline{ED} and \overline{BC}. What is the area of BFDG?

\textbf{(A)}\ \frac{133}{2}\qquad\textbf{(B)}\ 67\qquad\textbf{(C)}\ \frac{135}{2}\qquad\textbf{(D)}\ 68\qquad\textbf{(E)}\ \frac{137}{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.