2012 AMC 10B Problem 19

The polygon $BFDG$ is a trapezoid with bases $DG$ and $BF$ and height $6.$ Also, since $G$ is the midpoint between $A$ and $D,$ we have $GD= 15.$ We can see that $EBF \sim EAD ,$ so $$\dfrac{BF}{AD} = \dfrac{EB}{EA}$$ $$\dfrac{BF}{30} = \dfrac 28$$$$BF = 7.5$$ This makes the area of $BFDG$ equal to $\dfrac{6(15+7.5)}2 = \dfrac{135}2.$ Thus, the correct answer is C .