Area of an Equilateral Triangle

Area of an Equilateral Triangle

How to find the area of an equilateral triangle: formula, proof, example, and its solution.

Formula

If the length of an equilateral triangle's side is a, then the area of the equilateral triangle is (square root 3 / 4)*a^2.

If the equilateral triangle's side is a,
then the height of the equilateral triangle is
(√3/4)⋅a2.

Proof

The area of a triangle is (1/2)bh. b = a. And h = ((square root 3)/2)*a. So A = ((square root 3)/4)*a^2.

For the given equilateral triangle,
Base: b = a
Height: h = (√3/2)⋅a

Area: A = (1/2)⋅bh
= (1/2)⋅b⋅(√3/2)⋅a
= (√3/4)⋅a2

Example

Find the area of the given triangle. The length of the equilateral triangle's side: 6.

The equilateral triangle's side: 6

Area: A = (√3/4)⋅62