Home Geometry Problems All Problems 101-110 View or post a solution    By Antonio Gutierrez
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 Semiperimeter of  d, e, f, prove that the area S of triangle ABC is: Formula to Prove. Elearning.
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Equilateral area. Elearning, Online Tutoring.

 

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."


 USE

  • Congruence of Triangles SAS

  • Congruence of triangles SSS

  • Heron's formula of area of a triangle

  • Formula of the area of an equilateral triangle: Formula of the area of an equilateral triangle, where s is any side.

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