The perimeter of an equilateral triangle is 75 cm. Find its area.

$\frac{625\sqrt{3}}{4} cm^2$

We know that,

The perimeter of a equilateral triangle = 3(side)

And the area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (side)² 

We have,

Perimeter of a equilateral triangle = 75 cm

Then the side ,

3(side) = 75

side = 25cm

The area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (25)²

= \(\frac{\sqrt {3}}{4}\) × 625 = $\frac{625\sqrt{3}}{4} cm^2$