What is the area of an equilateral triangle that has a perimeter of 18 centimeters?

Jan 26, 2016

Area $= 9 \sqrt{3}$ sq. cm.

Explanation:

If the perimeter of an equilateral triangle is $18$ centimeters
$\textcolor{w h i t e}{\text{XXX}}$each side is $6$ centimeters long
and
$\textcolor{w h i t e}{\text{XXX}}$ the semi-perimeter, $s$, is $9$ centimeters long.

Using Heron's formula With sides $a = b = c = 6$ and $s = 9$
color(white)("XXX")"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))

$\textcolor{w h i t e}{\text{XXXXXXX}} = \sqrt{9 \times 3 \times 3 \times 3}$

$\textcolor{w h i t e}{\text{XXXXXXX}} = 9 \sqrt{3}$