# Problem #1415

 1415 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 $ABQCDP$? $\textbf{(A)}\ 28\sqrt {3}\qquad \textbf{(B)}\ 30\sqrt {3}\qquad \textbf{(C)}\ 32\sqrt {3}\qquad \textbf{(D)}\ 35\sqrt {3}\qquad \textbf{(E)}\ 36\sqrt {3}$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
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