HMMT 2002 U52

Guts
Answer

Let $A B C D$ be a quadrilateral, and let $E, F, G, H$ be the respective midpoints of $A B, B C, C D, D A$ . If $E G=12$ and $F H=15$ , what is the maximum possible area of $A B C D$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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