Perimeter of a triangle

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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:

Drawing of the scalene triangle

Formula for the perimeter of a scalene triangle

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

Drawing the 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).

Formula of the perimeter of an equilateral triangle

Perimeter of an Isosceles Triangle

Drawing of the isosceles triangle for calculating its perimeter

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).

Formula of the perimeter of an isosceles triangle

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).

Drawing of the isosceles triangle for the calculation of its perimeter by the law of cosines

Perimeter of a Scalene Triangle

Drawing of the 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:

Formula for the perimeter of a scalene triangle

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):

Formula for the perimeter of a scalene triangle knowing two sides and an angle

Perimeter of a Right Triangle

Right triangle drawing

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).

Formula for the perimeter of a right triangle

Drawing of the right triangle to calculate the perimeter by the Pythagorean theorem

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):

Formula for the perimeter of a right triangle through the Pythagorean theorem

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

Drawing of the equilateral triangle example 1 for perimeter calculation.

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

What is its perimeter?

Applying the above formula:

Example of the perimeter of an equilateral triangle.

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

2. Determine the Perimeter of an Isosceles Triangle

Example of isosceles triangle for calculating its perimeter

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.:

Example of calculating the perimeter of an isosceles triangle

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

3. Find the perimeter of a Scalene Triangle

Consider a given triangle:

Exercise 1 of scalene triangle to calculate its perimeter

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.

Calculating the perimeter of a scalene triangle

So, the perimeter is 9 cm.

4. Find the perimeter of a Right Triangle

Example of a right triangle to calculate its perimeter

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:

Solution in the example 1

The perimeter of the triangle is 12 cm.


AUTHOR: Bernat Requena Serra

YEAR: 2020


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