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 ill-structured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."