The drawing shows a triangle ABC, M is
the center of the square ABCD of area 32, N is the center of the
square BCEF of area 46, and MNPQ is a square of area 67. Find
the area of triangle ABC.
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."