Quadrilateral In Triangle

Geometry Level 5

In a triangle ABCABC, points DD and EE are on BCBC such that BD:DE:EC=1:1:1 | BD | : | DE | : | EC | = 1 : 1:1 , and points FF and GG are on ACAC such that AF:FG:GC=1:3:1 | AF | : | FG | : |GC | = 1 : 3 : 1 .

The quadrilateral PQRSPQRS is formed by the intersection of segments BF,BG,ADBF, BG, AD and AEAE.

If the area of the triangle ABC ABC is 1001 square units, what is the area of quadrilateral PQRSPQRS?

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