# 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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