How to Find the Perimeter of a Triangle

Finding the perimeter of a triangle means detecting the distance around the triangle. The easiest way to find the perimeter of a triangle is to add up the length of all 3 sides, but if you don’t know how to calculate different types of a triangle, then this blog post will teach you how to calculate the perimeter of a right triangle when only two of the side lengths are known.

Furthermore, it will explain solved examples of different types of a triangle so that you have a clear idea about them.

What is the Perimeter of a Triangle?

The perimeter of a triangle is the sum of all three sides. It is the combination of two Greek words; “peri” means around, and “metron” means measure. Thus, the total distance around any 2D shape is defined as its perimeter.

However,the perimeter gives the length of the boundary of a shape and is expressed in linear units.

Example of Triangular Park

Suppose we want to know the fence dimensions as shown below. So, we will add the lengths of all three sides of the park. Hence, this length or distance of the boundary of a triangle is known as the perimeter of the triangle.

Types of Triangles

The Perimeter of a Triangle Formula

The basic formula which is used to calculate the perimeter of a triangle is:

Perimeter = a + b + c (sum of the three sides)

How to Find the Perimeter of a Triangle?

1. Note the measurements of all the sides and check that all the 3 sides have the same unit.
2. Add all the sides.
3. Give the answer with the unit.

Let me show you an example of finding a triangle’s perimeter.

Example: Find the perimeter of a polygon whose sides are 10 cm, 8 cm, and 4 cm.

Solution: let,

a = 10 cm

b = 8 cm

c = 4 cm

Formula:

Perimeter = sum of the three sides

P = a+b+c

P = 10+8+4 = 22

Therefore, the answer is 22 cm.

How to Calculatethe Perimeter of a Scalene Triangle?

A scalene triangle is a type of triangle which is having all three sides of different lengths. So, the perimeter of a scalene triangle will be calculated by finding the sum of all the unequal sides. The formula is the same as P = a + b + c, where “a,””b,” and “c” are the three different sides lengths.

The Perimeter of an Isosceles Triangle

If a triangle has two sides with equal length and one side is different, it is said to be an Isosceles triangle. The perimeter of an isosceles triangle will be calculated by finding the sum of the equal and unequal sides.

Hence, the formula of the perimeter of an isosceles polygon = 2a + b units where,

• a = sides of equal length
• b = the third side of different length

The Perimeter of an Equilateral Triangle

If a triangle has all the sides of equal length, it is an Equilateral triangle. So, the formula for the perimeter of an equilateral polygon is:

P = (3 x a) units where

• a = length of each side of the triangle.

The Perimeter of a Right Triangle

If a triangle has one of the angles at 90 degree is called a right-angled triangle or a right triangle. The formula to find the perimeter of a right-angled triangle is:

P = a + b+ c units.

However, if any side of the right triangle is unknown, then we can use the Pythagoras theorem, which says that the square of the hypotenuse is equal to the sum of squares of the other two sides. By Pythagoras’ theorem, we have

 c² = a² + b²

In this case, we can also be written the perimeter of a right triangle as P = a + b + √ (a²+b²). This is because c² = a² + b², therefore, c = √(a² + b²).

Where,

• a = Perpendicular
• b = Base
• c = Hypotenuse ( the longest side and opposite to the right angle)

So, for example, if you know side a = 3 cm and side b = 4 cm, then put those values into the formula as follows:

c² = 3² + 4²

^c2= 9 + 16

^c2= 25

Taking square root on both sides, we obtain

√^c2= √25

c = 5 cm

Now, add the length of all three sides to find the perimeter. P = a + b + c = 3 + 4 + 5 = 12 cm.                                

The Perimeter of Isosceles Right Triangle

If a right-angled triangle has two equal sides and two equal angles, it is called an isosceles right triangle. The formula to calculate the perimeter of an isosceles right triangle is P = 2l + h, where l is the length of two equal sides, and h is the hypotenuse.

Conclusion

Hopefully, you have got the entire concept of Perimeter of a triangle, its types, and how to calculate them.

Let us know if you have any further queries. We are glad to help you!