# Height of an Equilateral Triangle

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

## Equilateral Triangle

An equilateral triangle is a triangle

whose sides are all congruent.

(Its name explains itself: [equi] + [lateral].)

Its interior angles are also all congruent: 60º.

## Formula

*h* = (√3/2)⋅*a**h*: Height of an equilateral triangle*a*: Side of an equilateral triangle

## Example 1

The equilateral triangle's side is 8.

And its height is *x*.

So, by the height formula,*x* = (√3/2)⋅8.

8/2 = 4

So *x* = 4√3.

## Example 2

The equilateral triangle's side is *x*.

And its height is 12.

So, by the height formula,

12 = (√3/2)⋅*x*.

Switch both sides.

Divide both sides by √3/2.

Then *x* is equal to

12 times, the reciprocal of √3/2, 2/√3.

To remove the square root in the denominator,

multiply [√3/√3].

Then *x* = 24√3/3.

Rationalizing the denominator

24/3 = 8

So *x* = 8√3.