# Perimeter of a triangle

The **perimeter of a triangle** is the sum of its three sides.

The formula for the **perimeter of a triangle** depends on the type of triangle. But there is a general formula to calculate it:

Let’s see how we can calculate the perimeter of the equilateral triangle, isosceles triangle, scalene triangle and right triangle.

## Perimeter of an Equilateral Triangle

An **equilateral triangle** has all three sides equal, so its **perimeter** will be three times the length of one of its sides (*a*).

## Perimeter of an Isosceles Triangle

The **perimeter of an isosceles triangle** is obtained as the addition of the three sides of the triangle. Having two equal sides, the perimeter is twice the repeated side (*a*) plus the different side (*b*).

In an isosceles triangle, if the repeating side (*a*) and the angle they form are known, the other side (*b*) should be found by **Law of Cosines** (**Cosine Rule**).

## Perimeter of a Scalene Triangle

A scalene triangle is a triangle in which all three sides are in different lengths. The **perimeter of a scalene triangle** with three unequal sides is determined by adding the three sides.

If you know the length of the three sides, it’s easy to calculate its perimeter using the following formula:

If you know two sides of the triangle and the angle they form you can solve for the missing side using the Law of Cosines (Cosine Rule):

## Perimeter of a Right Triangle

The perimeter of a right triangle is the sum of the lengths of the two legs and the hypotenuse (in other words, the sum of all three sides).

If both legs (*a* and *b*) are known, their perimeter can be calculated from them. This is because thanks to **Pythagorean theorem**, the hypotenuse (*c*) can be expressed in terms of the legs (*a* and *b*):

Download this **calculator** to get the results of the formulas on this page. Choose the initial data and enter it in the upper left box. For results, press ENTER.

Triangle-total.rar or Triangle-total.exe

Note. Courtesy of the author: **José María Pareja Marcano**. Chemist. Seville, Spain.

## Exercises

### 1. Find the Perimeter of an Equilateral Triangle

Being a **equilateral triangle** with all sides equal in length *a*=5 cm.

What is its **perimeter**?

Applying the above formula:

We obtain that the perimeter of this equilateral triangle is **15 cm**.

### 2. Determine the Perimeter of an Isosceles Triangle

Being an **isosceles triangle** with two equal sides, *a*=3 cm and a different side of *b*=2 cm.

What is its **perimeter**?

To calculate this **perimeter** we add the repeated side multiplied by two plus the unequal side, i.e.:

It is obtained that the isosceles triangle’s **perimeter** is **8 cm**.

### 3. Find the perimeter of a Scalene Triangle

Consider a given triangle:

Let be a **scalene triangle** of known sides, these being *a*=2 cm, *b*=4 cm and *c*=3 cm.

What is its **perimeter**? This will be calculated as the sum of its three sides.

So, the **perimeter** is **9 cm**.

### 4. Find the perimeter of a Right Triangle

We can find the perimeter of a right triangle whose sides are *a*=3 cm, *b*=4 cm and *c*=5 cm by adding all the three sides:

The perimeter of the triangle is **12 cm**.