Question 25
Let $ABCD$ be a trapezoid with $AB \parallel CD,$ $AB = 11,$ $BC = 5,$ $CD = 19,$ 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 $ABQCDP?$