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:$$S=\dfrac{1}{2} (\dfrac{d^2\sqrt 3}{4}+\dfrac{e^2\sqrt 3}{4}+\dfrac{f^2\sqrt 3}{4}+3\sqrt {s(s-d)(s-e)(s-f)} )$$.       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: , where s is any side. Recent Additions