Height of an Equilateral Triangle

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 interior angles are all congruent: 60 degrees.

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 = (sqrt[3]/2)*a. h: Height of an equilateral triangle, a: Side of an equilateral triangle.

h = (√3/2)⋅a

h: Height of an equilateral triangle
a: Side of an equilateral triangle

Example 1

Find the value of x. The length of the equilateral triangle's side: 8. The height of the equilateral triangle: x.

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

Find the value of x. The length of the equilateral triangle's side: x. The height of the equilateral triangle: 12.

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.