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 denominator3
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.