Online Geometry Problem 771: Area of a Parallelogram, Star, Pentagon,
Triangles. Level: High School, College,
Mathematics Education
In the figure below, ABCD is a parallelogram
of area S. G is on BC, F on AD and E an exterior point. Lines EA, EB,
AG, BF, and FG determine the shaded regions of areas S1, S2, S3, S4, S5,
and S6. Prove: S1 + S2 + S3 + S4
+ S5
-S6-= S/2.