A geometry problem by Ajay Sambhriya

Geometry Level 4

The rectangle \(ABCD\) have dimension \(6\times 4\) with \(AB = 6, BC = 4\) and \( HG \parallel AB \), where \(G\) is a midpoint of \(AC\) if \( \dfrac{GF}{FA} = \dfrac21\).

Find the area of the shaded region.

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