In rectangle $ABCD$, $AB=10$, $AD=24$, and $G$ is a point on $\overline{AD}$ such that $AG=\frac{1}{3}AD$. Segment $AB$ is extended 5 units beyond $B$ to point $E$, and $F$ is the intersection of $\overline{ED}$ and $\overline{BC}$. What is the area of $BFDG$?