# The perimeter of an equilateral triangle is 24. What is the area?

Apr 27, 2016

The area  = color(green)(16sqrt3 cm^2

#### Explanation:

The perimeter of an equilateral triangle $\left(3 a\right)$ is $= 24 c m$ (assuming units to be in cm)

Let us denote the side of the equilateral triangle as $a$

$3 a = 24$

$a = \frac{24}{3}$

color(green)(a = 8cm

The formula for area of equilateral triangle is :
color(blue)(sqrt3/4 (a^2)

$= \frac{\sqrt{3}}{4} \left({8}^{2}\right)$

$= \frac{\sqrt{3}}{4} \cdot 64$

 = color(green)(16sqrt3 cm^2