AMC 12 2008b Problem 25

Let $ABCD$ be a trapezoid with $AB||CD$, $AB = 11$, $BC = 5$, $CD = 19$, and $DA = 7$. Bisectors of $\angle A$ and $\angle D$ meet at $P$, and bisectors of $\angle B$ and $\angle C$ meet at $Q$. What is the area of hexagon $ABQCDP$?

(Solution)

\textbf{(A)}\ 28\sqrt {3} \textbf{(B)}\ 30\sqrt {3} \textbf{(C)}\ 32\sqrt {3} \textbf{(D)}\ 35\sqrt {3} \textbf{(E)}\ 36\sqrt {3}