PRINCIPIA · THEOREM

Equilateral area = (√3/4)·a²

Dependencies: Triangle area = ½ × base × height (J.03), 30-60-90 triangle side ratios (D.09).

Statement

Let $\triangle ABC$ be an equilateral triangle with side length $a$ (i.e. $|AB|=|BC|=|CA|=a$ ). Then its area is

S_{\triangle ABC} \;=\; \tfrac{\sqrt{3}}{4}\,a^{2}.

$Equilateral \triangle ABC with side a + altitude AH + formula S=\tfrac{\sqrt{3}}{4}a^{2}.$

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