Hexagon AreaGeometry 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.