Problem 102. Equilateral Triangle Area, Interior Point.
Level: High School, College, SAT Prep.

In the figure below, given an equilateral triangle ABC, D is an interior point. If AD = 5, BD = 4, and CD = 3, find 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."