Perimeter of Triangle – Concept, Formula, Examples, FAQ

What is the Perimeter of a Triangle?

The perimeter of a triangle represents the sum of all three sides of the triangle. The total length of any two-dimensional figure is called its perimeter.

The Perimeter of a Triangle Formula

We can calculate the perimeter of a triangle by adding the lengths of the three given sides.

So, the perimeter of triangle formula = sum of the lengths of three sides of the triangle.

Now we will understand this formula for the different types of triangles.

The Perimeter of the Scalene Triangle

A scalene triangle has three sides measuring different lengths. We can calculate the perimeter of a scalene triangle by calculating the sum of all the sides. 

The formula for the perimeter of a scalene triangle = (a + b + c), where a, b, and c are the lengths of the sides of the triangle.

The Perimeter of the Isosceles Triangle

A triangle that has two sides of the same length and one side of a different length is called an isosceles triangle. We can calculate the perimeter of an isosceles triangle by finding the sum of its sides. 

The formula for the perimeter of an isosceles triangle = (l + l + b) = (2l + b)

Where,

l = length of equal sides

b = length of the third side

The Perimeter of the Equilateral Triangle

If a triangle has all the sides of equal measure, it is an equilateral triangle. We can calculate the perimeter of an equilateral triangle by the formula given below:

The perimeter of an equilateral triangle = (a + a + a) = (3 × a)

Where, a = length of any of the sides of the equilateral triangle.

The Perimeter of a Right-Angled Triangle

A right-angled triangle has one of the angles as 90º. We can calculate the perimeter of a right-triangle by adding the length of its sides. 

The formula to calculate the perimeter of a right-angled triangle is:

Perimeter of a right-angled triangle = (a + b + c)

Where a, b, and c = the lengths of the sides

Since this is a right-angled triangle, we can use the Pythagoras theorem to find the length of any side which is not known. From the figure given above:

a = Perpendicular of the right triangle

b = Base of the right triangle

c = Hypotenuse of the right triangle

Hence, using the Pythagoras theorem, we get 

c^{2}=a^{2}+b^{2}
\text { or } c=\sqrt{( a^{2}+b^{2})}

Now, we can write the perimeter of a right triangle as

=\left\{a+b+\sqrt{\left(a^{2}+b^{2}\right)}\right\}

Examples 

1. Find the perimeter of a triangle if the sides are 6 cm, 5 cm, and 3 cm?

Solution: Since all the three sides are unequal, it is a scalene triangle.

Let,

a = 6 cm

b = 5 cm

c = 3 cm

perimeter of a scalene triangle = (a + b + c) = 6 +5 + 3 = 14

Therefore, the answer is 14 cm.

2.  Find the perimeter of a triangle if each side is 10 cm?

Solution: Since all three sides are equal in length, this is an equilateral triangle.

Which means a = b = c = 10 cm.

Perimeter of an equilateral triangle 

= a + b + c

= 10 + 10 + 10

= 30 cm

Therefore, the answer is 30 cm.