# What is the area of an equilateral triangle with a perimeter of 6 inches?

May 14, 2018

$A$ = $\sqrt{3}$

#### Explanation:

An equilateral triangle has $3$ sides and all the measures of its sides will be equal. So, if the perimeter, the sum of the measure of its sides, is $6$, you must divide by the number of sides, $3$, to get the answer:

$\frac{6}{3}$ = $2$, so each side is $2$ inches.

$A = \frac{{a}^{2} \sqrt{3}}{4}$, where $a$ is the side. Plug in your variable, $2$.

$A$ = $\frac{{2}^{2} \sqrt{3}}{4}$

$A = \left(\textcolor{red}{\cancel{\textcolor{b l a c k}{\text{4")))sqrt(3))/(color(red)(cancel(color(black)("4}}}}\right)$

$A$ = $\sqrt{3}$