How to find Area of an Equilateral Triangle if its Perimeter is given

QUESTION: If the perimeter of an equilateral triangle is 30 cm, what is its area?

SOLUTION:

Equilateral triangles are those triangles whose all sides have same length.

Formula of Area of an Equilateral Triangle = $\frac{\sqrt3}4(s)^2$ ———(1)

where $s$ is the length of each side of an Equilateral Triangle.

Here,

Perimeter of an Equilateral Triangle = 30 cm

Then

Length of each side of this triangle = $s$ = $\frac{30}3$ ⇒10 cm

Put this value of $s$ in equation (1) to find area

Area of an equilateral triangle = $\frac{\sqrt3}4(10)^2$

= 43.3 cm²

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