2.2.8 Equilateral Triangle Formulas

Formulas for an equilateral triangle with side length $s$ and height $h$:

Property	Formula
Area (given side s)	$A = \frac{s^2\sqrt{3}}{4}$
Area (given height h)	$A = \frac{h^2\sqrt{3}}{3}$
Height (given side s)	$h = \frac{s\sqrt{3}}{2}$

Example: An equilateral triangle’s perimeter is 12. Its area is $4k\sqrt{3}$. What is k? $s = 12/3 = 4 \Rightarrow A = \frac{4^2\sqrt{3}}{4} = 4\sqrt{3} \Rightarrow k = 1$

Example: An equilateral triangle has a height of 4, what is its side length? $h = 4 = \frac{s\sqrt{3}}{2} \Rightarrow s = \frac{8}{\sqrt{3}} = \frac{8\sqrt{3}}{3}$

Problem Set 2.2.8