Right Triangles Galore

Geometry Level 3

From the figure below, \( ABC\) and \(DEF\) are right triangles, and \(AF\) and \(DC\) are the their respective altitudes. Point \(G\) is the intersection of \(AC\) and \(DF\) and \(GH\) is drawn from it such that it is perpendicular to \(BC\). If \(AF = 6\) and \(GH = 4\) and \(FC = 9\), what is the area of polygon \(AGDEB\)?

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