# Equilateral Triangle Formula

By the end of this lesson, you will be able to

- define equilateral triangle.
- derive the formula for the perimeter and area of an equilateral triangle.
- calculate the perimeter and area.
- represents examples of equilateral triangle.
- relate the equilateral triangle to isosceles and scalene triangle.

## Equilateral Triangle

A triangle is said to be equilateral triangle if its three sides are of equal length.

An equilateral triangle

Another way...

The triangle in which all three internal angles are equal in measure is called equilateral triangle. Again, an equilateral triangle can be defined as.., the triangle having each angle is equal to 60° in measure is called an equilateral triangle.

As the sum of three angles of an equilateral triangle adds up to 180° and each angle is equal to one another, therefore each angle is equal to 60° in measure.

An equilateral triangle is a special triangle.

It is a regular polygon of three sides.

Therefore, it is a regular triangle.

All three sides are of equal length.

The height from any vertex to the base is h = √32 a where a is the side of the equilateral triangle.

## Primeter of Equilateral Triangle

Let AB = BC = AC = a unit in equilateral △ABC.

If the perimeter is P,

P = (a + a + a) unit

∴ P = 3a unit

### Example Equilateral Triangle

## Area of Equilateral Triangle

Suppose, AB = BC = AC = a unit in equilateral △ABC

Draw a perpendicular AD from the vertex A to the base BC i.e. AD⊥BC.

∴ BD = 12 BC

∴ BD = a2

From the right △ABD, it can be written by the Pythagorean theorem

AD^{2} = AB^{2} - BD^{2}

or, AD^{2} = a^{2} - a^{2}4

or, AD^{2} = 4a^{2} - a^{2}4

or, h^{2} = 3a^{2}4

or, h = √3a^{2}√4

or, h = √32 a

∴ △ABC = 12 BC . h

or, △ABC = 12 a . √32 a

∴ △ABC = √34 a^{2}

If the length of the side is a and the area is A of an equilateral triangle,

A = √34 a^{2} square unit