Geometry · Equilateral triangle · 30 60 90 triangle · Foot of perpendicular · Triangle area
The equilateral triangle \(ABC\) has sides of length \(4\) cm. Let \(D\) be the midpoint of the side \(AB\), and let \(E\) and \(F\) be the feet of the perpendiculars dropped from \(D\) to the sides \(BC\) and \(AC\). Compute the area of the triangle \(DEF\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2008, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source