The area of a triangle ABC is 24. D,
E, and F are the midpoints of BC, AC, and AB, respectively.
Perpendiculars from E to AB and F to AC meet at G,
perpendiculars from F to BC and D to AB meet at H,
perpendiculars from D to AC and E to BC meet at M. Find the area
of the hexagon DMEGFH.
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 illstructured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."
