# Equilateral Triangle: Height

How to find the height of an equilateral triangle: formula, 2 examples, and their solutions.

## Equilateral Triangle

### Definition

An equilateral triangle is a triangle

whose sides are all congruent.

Its interior angles are also all congruent: 60º.

## Formula

### Formula

h = [√3/2]⋅a

h: Height of an equilateral triangle

a: Side of an equilateral triangle

## Example 1

### Example

### Solution

The given triangle is an equilateral triangle.

Its side is 8.

Its height is x.

Then x = [√3/2]⋅8.

Cancel the denominator 2

and reduce 8 to, 8/2, 4.

So x = 4√3.

## Example 2

### Example

### Solution

The given triangle is an equilateral triangle.

Its side is x.

Its height is 12.

Then 12 = [√3/2]⋅x.

Switch both sides.

Multiply, the reciprocal of √3/2, 2/√3

to both sides.

Then x = 12⋅[2/√3].

Rationalize the denominator √3

by multiplying √3/√3.

12⋅2⋅√3 = 24√3

√3⋅√3 = 3

Then x = 24√3/3.

Cancel the denominator 3

and reduce the numerator to, 24/3, 8.

So x = 8√3.