HMMT 2014 U19

Let $A B C D$ be a trapezoid with $A B \| C D$. The bisectors of $\angle C D A$ and $\angle D A B$ meet at $E$, the bisectors of $\angle A B C$ and $\angle B C D$ meet at $F$, the bisectors of $\angle B C D$ and $\angle C D A$ meet at $G$, and the bisectors of $\angle D A B$ and $\angle A B C$ meet at $H$. Quadrilaterals $E A B F$ and $E D C F$ have areas 24 and 36, respectively, and triangle $A B H$ has area 25 . Find the area of triangle $C D G$.