# What is the Area of an Equilateral Triangle with a height of 9 inches?

A triangle that has all three equal sides along with equal angles is known as an equilateral triangle.

## Answer: The area of an equilateral triangle with a height of 9 inches is equal to 27√3 square inches.

Let us look into the step-by-step solution.

**Explanation:**

The area of an equilateral triangle with side length 'a' is given by,

Area = √3 a^{2}/ 4

The height of an equilateral triangle is given by,

h = (a × √3) / 2

Thus,

a = 2h / √3

where,

- 'a' is the measure of each side of the triangle.
- 'h' is the height of the triangle

We have 'h' = 9 inches

Substituting the value of 'h' in the formula, let's calculate the value of 'a' as shown below

a = 2h / √3

= (2 × 9) / √3

** **= 18/√3

** **= 6√3 inches

Thus, substituting the value of 'a' in the area formula we get,

Area = (√3 × 6√3 × 6√3 ) / 4

= (36 × 3 × √3)/4

= 27√3 square inches

### Thus, the area of an equilateral triangle with a height of 9 inches is equal to 27√3 square inches.