2002 AIME I Problem 10

In the diagram below, angle A B C is a right angle. Point D is on \overline{B C}, and \overline{A D} bisects angle C A B. Points E and F are on \overline{A B} and \overline{A C}, respectively, so that A E=3 and A F=10. Given that E B=9 and F C=27, find the integer closest to the area of quadrilateral D C F G.