How to find the area of an equilateral triangle if one of its sides is known.

The area of a triangle is half the product of the base and the height. Height divides the base of an equilateral triangle in half. Let’s say the length of a side of a triangle is l. Then the length of the height h, according to the Pythagorean theorem, will be equal to:

h = √ (l ^ 2 – (0.5l) ^ 2) = (√3) / 2 l;

The area of the triangle will be equal to:

S = l × (√3) / 2 l = (√3) / 2 l ^ 2.