# Equilateral Triangle Formula

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## What is an Equilateral Triangle?

• As the name suggests, ‘equi’ means equal, and an equilateral triangle is the one in which all sides are equal.

• The internal angles of any given equilateral triangle are of the same measure, that is, equal to 60 degrees.

### What is the Area of Equilateral Triangle Formula?

The area of an equilateral triangle is the amount of space that it occupies in a 2-dimensional plane. To recall, an equilateral triangle can be defined as a triangle in which all the sides are equal and the measure of all the internal angles is 60°. So, an equilateral triangle’s area can be calculated if the length of any one side of the triangle is known.

### The Perimeter of Equilateral Triangle Formula

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

Here is a list of the area of the equilateral triangle formula, the altitude of the equilateral triangle formula, the perimeter of the equilateral triangle formula, and the semi-perimeter of an equilateral triangle.

### Formulas and Calculations for an Equilateral Triangle:

• Perimeter of Equilateral Triangle: P = 3a

• Semiperimeter of Equilateral Triangle Formula: s = 3a/2

• Area of Equilateral Triangle Formula: K = (1/4) * √3 * a2

• The altitude of Equilateral Triangle Formula: h = (1/2) * √3 * a

• Angles of Equilateral Triangle: A = B = C = 60 degrees

• Sides of Equilateral Triangle: a equals b equals c.

1. Given the side of the triangle find the perimeter, semiperimeter, area, and altitude.

• a is known here; find P, s, K, h.

• P equals 3a

• s = 3a/2

• K = (1/4) * √3 * a2

• h = (1/2) * √3 * a

2. Given the perimeter of triangle find the side, semiperimeter, area, altitude.

• Perimeter(P) is known; find a, s, K, and h.

• a = P/3

• s = 3a/2

• K = (1/4) * √3 * a2

• h = (1/2) * √3 * a

3. Given the semi perimeter of a triangle find the side, perimeter, area, and altitude.

• Semiperimeter (s) is known; find a, P, K, and h.

• a = 2s/3

• P = 3a

• K = (1/4) * √3 * a2

• h = (1/2) * √3 * a

4. Given the area of the triangle find the side, perimeter, semiperimeter, and altitude.

• K is known; find a, P, s and h.

• a = √[(4 / √3) * K] equals 2 * √[K/√3]

• P = 3a

• s = 3a / 2

• h = (1/2) * √3 * a

5. Given the altitude/height find the side, perimeter, semiperimeter, and area

• Altitude (h) is known; find a, P, s, and K.

• a = (2/√3) * h

• P = 3a

• s = 3a/2

• K = (1/4) * √3 * a2

### Solved Examples

Question 1) Suppose you have an equilateral triangle with a side of 5 cm. What will be the perimeter of the given equilateral triangle?

Solution) We know that the formula of the perimeter of an equilateral triangle is 3a.

Here, a = 5 cm

Therefore, Perimeter = 3 * 5 cm = 15 cm.