Question

If the perimeter of the equilateral triangle is $180$ $cm$, what will be its area?

Answer 1

Calculate the area of equilateral triangle

Given: Perimeter of equilateral triangle $180$ $cm$

We know that,

All sides of an equilateral triangle are equal in measure.

Step $1$:-

Let $a$ be the side of equilateral triangle.

Then, perimeter of a equilateral triangle $=3a$

Now,

$$\begin{gathered} \Rightarrow 3a=180 \\ \Rightarrow a=\frac{180}{3} \\ \Rightarrow a=60cm \end{gathered}$$

Step $2$:-

Area of equilateral triangle $=\frac{\sqrt{3}}{4}{a}^2$

$$\begin{gathered} =\frac{\sqrt{3}}{4}{\left(60\right)}^2 \\ =900\sqrt{3}c{m}^2 \\ =1558.84c{m}^2 \end{gathered}$$

Hence, if the perimeter of the equilateral triangle is $180$ $cm$, then its area is $1558.84c{m}^2$.