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 \(DCFG\).

(第二十届AIME1 2002 第10题)