A good geometry problem

Geometry Level 5

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 \(DCFG\).

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