Apply Ceva's Theorem, I Don't Think

Geometry Level 5

Let there be a triangle \(ABC\) with \(AD\) being a line passing through \(A\) intersecting \(BC\) (not extended) at \(D\) and \(BE\) being the line passing through \(B\) and intersecting \(AC\) (not extended) at \(E\) let the intersection of \(AD\) and \(BE\) be \(H\).

If the area of \(\Delta AHE\) be \(2\), the area of \(\Delta AHB\) be \(3\) and the area of \(\Delta BHD\) be \(4\). Find the area of \(CDHE\).

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