Area of Equilateral Triangle

Theorem
Let $T$ be an equilateral triangle.

Let the length of one side of $T$ be $s$.

Let $\AA$ be the area of $T$.

Then:
 * $\AA = \dfrac {s^2 \sqrt 3} 4$

Proof

 * Area-of-Equilateral-Triangle.png

From Area of Triangle in Terms of Two Sides and Angle:


 * $\AA = \dfrac {s^2} 2 \sin 60 \degrees$

From Sine of $60 \degrees$:


 * $\sin 60 \degrees = \dfrac {\sqrt 3} 2$

The result follows.