# Area of an Equilateral Triangle

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

## Formula

If the equilateral triangle's side is *a*,

then the height of the equilateral triangle is

(√3/4)⋅*a*^{2}.

## Proof

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)⋅*a*^{2}

## Example

The equilateral triangle's side: 6

Area: *A* = (√3/4)⋅6^{2}