Geometry Problem 103. Equilateral Triangle Area, Interior Point, Heron.
Level: High School, College, SAT Prep.
In the figure below, given an
equilateral triangle ABC, D is an interior point. If
AD = d, BD = e, CD = f, and
,
prove that the area S of triangle ABC is:
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 illstructured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given." USE

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