What is an Equilateral Triangle?

As the name itself indicates, 'equi' means equal, an equilateral triangle is that in which all three sides are equal. The internal angles of any given equilateral triangle are equal to 60 degrees. 

Triangles are classified into three types based on the length of their sides:

Scalene Triangle: The sides as well as the angles of the scalene triangle are not equal.

Isosceles Triangle: An isosceles triangle has two equal sides and two equal angles.

Equilateral Triangle: All sides and angles of the equilateral triangle are equal.

Area of Equilateral Triangle

Area of an Equilateral Triangle An equilateral triangle is defined by the region enclosed by three sides. It is measured as square units. The commonly used measures for the area of an equilateral triangle are,

Further below the area formula of the equilateral triangle, we have the altitude of the equilateral triangle formula, the perimeter of the equilateral triangle formula, and the semi-perimeter of an equilateral triangle.

Area Formula of an Equilateral Triangle

The area of an equilateral triangle is that which it encloses in a two-dimensional space. Recall that an equilateral triangle is described as a triangle where all sides are congruent, that is, having all interior angles measured at 60°. Hence, the area of an equilateral triangle can be computed if the length of any one side of the triangle is known.

The formula of area of an equilateral triangle is used to find the area between the sides of an equilateral triangle in a plane.

The formula to calculate the area of a triangle with known base and height:

Area = 1/2 × base × height

The following formula can be used to find the area of an equilateral triangle:

Formula for the Perimeter of an Equilateral Triangle

The perimeter is the sum of the length of three sides of a triangle, whether equal or not.

A triangle will be equilateral if all its sides are the same; and the perimeter of an equilateral triangle is simply a sum of the three equal sides.

Basic Formula for the Perimeter of an Equilateral Triangle P = 3a, where 'a' is the length of the single side of the triangle. Adding up would be a + a + a = 3a as all three sides of an equilateral triangle are equal.

Formulas for Equilateral Triangle

Equilateral Triangle Perimeter: 

Equilateral Triangle Semiperimeter Formula: 

Area of Equilateral Triangle Formula: 

The altitude of Equilateral Triangle Formula: 

Angle of Equilateral Triangle: 

Side of Equilateral Triangle: 

Solved example

Q.1: Use the equilateral triangle area formula and calculate the area of an equilateral triangle if each of its sides is 12 in.

Solution:

Side = 12 in

Using the equilateral triangle area formula,

Q.2: Calculate the perimeter and semi perimeter of an equilateral triangle with a side measurement of 12 units.

Solution:

The perimeter  = 3a 

Semi-perimeter = 3a/ 2

Given, side a = 12 units

Now, the perimeter of an equilateral triangle is equal to:

3 × 12 = 36 units

And, Semi-perimeter of an equilateral triangle is equal to:

36/2 = 18 units.

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