2025 AIME I Problems/Problem 2

Problem

In $\triangle ABC$ points $D$ and $E$ lie on $\overline{AB}$ so that $AD < AE < AB$ , while points $F$ and $G$ lie on $\overline{AC}$ so that $AF < AG < AC$ . Suppose $AD = 4$ , $DE = 16$ , $EB = 8$ , $AF = 13$ , $FG = 52$ , and $GC = 26$ . Let $M$ be the reflection of $D$ through $F$ , and let $N$ be the reflection of $G$ through $E$ . The area of quadrilateral $DEGF$ is $288$ . Find the area of heptagon $AFNBCEM$ , as shown in the figure below.

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2025 AIME I Problems/Problem 2

Problem