What is the area of an equilateral triangle with a height of 9 inches?

Solution:

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

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

Area = √3 a²/ 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.

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What is the area of an equilateral triangle with a height of 9 inches?

Summary:

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