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   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 \(s=\dfrac{d+e+f}{2}\), prove that the area S of triangle ABC is:
\(S=\dfrac{1}{2} (\dfrac{d^2\sqrt 3}{4}+\dfrac{e^2\sqrt 3}{4}+\dfrac{f^2\sqrt 3}{4}+3\sqrt {s(s-d)(s-e)(s-f)} )\).
 
 

Equilateral area. Elearning, Online Tutoring.

 


 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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