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

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.

$\blacksquare$