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.
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."
Area of a triangle