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.
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.
AUTHOR: Bernat Requena Serra