Let A B C D be a trapezoid with A B \| C D, A B=11, B C=5, C D=19, and D A=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 A B Q C D P ?
Answer Choices
A. 28 \sqrt{3}
B. 30 \sqrt{3}
C. 32 \sqrt{3}
D. 35 \sqrt{3}
E. 36 \sqrt{3}