Problem 398: Parallelogram, Area, Similarity,
Congruence

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 S_{1} is
the area of quadrilateral MNPQ, prove that S_{1} = S/13. .

Geometric Art: Hyperbolic Kaleidoscope of problem
398 using iPad Apps