Problem 398: Parallelogram, Area, Similarity,
The figure shows a parallelogram ABCD of
area S. AE = CF = AB/3, BG = DH = BC/3. Line CE intersects BH at M, and
DG at N. Line AF intersects DG at P, and BH at Q. If S1 is
the area of quadrilateral MNPQ, prove that S1 = S/13. .