In the figure below, prove that the area S₁ of the central hexagonal region DEFGHM determined by trisection of each side of a triangle ABC and connecting the corresponding points A', A", B', B", C', and C" with the opposite vertex is given by 1/10 the area of triangle ABC. Post a comment.

FACTS AND HINTS:

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

See also: