# Height of an Equilateral Triangle

How to find the height of an equilateral triangle: definition, formula, proof, examples, and their solutions.

## Equilateral Triangle

An equilateral triangle is a triangle

whose sides are all congruent.

(See its name: 'equi' + 'lateral'.)

Its interior angles are also all congruent: 60º.

## Formula

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

then the height of the equilateral triangle is

(√3/2)⋅*a*.

## Proof

See the left half of the equilateral triangle (blue).

The measures of its interior angles are 60 and 90.

So this is a 30-60-90 triangle.

Draw a 30-60-90 triangle

next to the equilateral triangle.

(with its sides → 1 : √3: 2)

The right triangles are similar.

So set a proportion

between the right triangles' corresponding sides:*h* / √3 = *a* / 2.

Similarity of sides in triangles

## Example 1

The equilateral triangle's side: 8

Height: *h* = (√3/2)⋅8

## Example 2

The equilateral triangle's side: *x*

Height: 12 = (√3/2)⋅*x*