a+b

In rectangle $ABCD$ , $AB=6$ , $AD=30$ , and $G$ is the midpoint of $AD$ . Segment $AB$ is extended $2$ units beyond $B$ to point $E$ , and $F$ is the intersection of $ED$ and $BC$ . If the area of $BFDG$ can be expressed in the form $\frac{a}{b}$ , where $a$ and $b$ are coprime, positive integers, what is $a+b$ ?