# Geometry Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals

Given a quadrilateral ABCD with midpoints E and F on sides BC and AD, respectively, AE intersects BF at G, and DE intersects CF at H.
If the area of triangle ABG is 9 and the area of the quadrilateral GEHF is 21, find the area of triangle CHD.

**Problem 1536**

Midpoints, lines meet,

Quadrilateral secrets,

Area revealed sweet.

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