Prove that the area of an equilateral triangle is .

Given: Side of an equilateral triangle.

To Prove: the area of an equilateral triangle is .

Concept Used:

If sides of a triangle are a, b, and c, then area of a triangle is given by:

Where s = semiperimeter of the triangle

Assumption: Let the side of triangle = x cm.

Explanation:

We know that all sides of an equilateral triangle are equal.

Therefore,

Now,

Hence, Proved.