2008 AMC 12B 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?

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

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