Question 10
In the diagram below, angle $ABC$ is a right angle. Point $D$ is on $\overline{BC},$ and $\overline{AD}$ bisects angle $CAB.$ Points $E$ and $F$ are on $\overline{AB}$ and $\overline{AC},$ respectively, so that $AE = 3$ and $AF = 10.$ Given that $EB = 9$ and $FC = 27,$ find the integer closest to the area of quadrilateral $DCFG.$
