# Hexagon Area

Geometry Level 3

Triangle $$ABC$$ has area $$[ABC] = 468$$. $$D, E$$ and $$F$$ are the midpoints of $$BC, CA$$ and $$AB$$, respectively. Points $$P, Q$$ and $$R$$ are defined such that $$P$$ is the incenter of $$AEF$$, $$Q$$ is the incenter of $$BFD$$, and $$R$$ is the incenter of $$CDE$$. What is $$[DREPFQ]$$?

Details and assumptions

$$[PQRS]$$ denotes the area of figure $$PQRS$$.

The incenter of a triangle is the center of the circle which is inscribed in the triangle such that it is tangent to all 3 sides.

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