Quadrilateral In Triangle

Geometry Level 5

In a triangle \(ABC\), points \(D\) and \(E\) are on \(BC\) such that \( | BD | : | DE | : | EC | = 1 : 1:1 \), and points \(F\) and \(G\) are on \(AC\) such that \( | AF | : | FG | : |GC | = 1 : 3 : 1 \).

The quadrilateral \(PQRS \) is formed by the intersection of segments \(BF, BG, AD\) and \(AE\).

If the area of the triangle \( ABC\) is 1001 square units, what is the area of quadrilateral \(PQRS\)?

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