Perimeter of Triangle

The perimeter of a triangle is the total length of its three sides. A triangle is a polygon with three sides, three vertices, and three angles. It is the simplest closed polygon in geometry, as it is the first possible closed figure. Any polygon can be divided into triangles. For instance, a quadrilateral can be divided into two triangles using a diagonal, and a pentagon into three triangles using diagonals from the same vertex.

Perimeter of Triangle Formula

For a triangle with sides a, b, and c, the perimeter P is:

P = a + b + c

Real-Life Example of Perimeter of Triangle:

The perimeter of a triangle is used to calculate the length of wire used to fence any triangular field. It is also used to build triangular furniture, tables, and other objects.

Parameter of Different Types of Triangles

Perimeters of various Types of Triangles can be found using the various variations of the perimeter formula which are mentioned below:

Perimeter of a Scalene Triangle

The perimeter of a triangle is equal to the sum of all sides of a triangle. Any triangle with three unequal sides is known as the Scalene Triangle. If the sides of a triangle have lengths equal to a, b, and c, then,

Read More: Scalene Triangle

Perimeter of an Isosceles Triangle

For an isosceles triangle, i.e., any triangle with two sides equal, let two equal sides be of length 'b' units and the length of the unequal side equals 'c', then, 

Read More: Isosceles right triangle

Perimeter of an Equilateral Triangle

For an equilateral triangle, since all sides are equal in length, thus a = b = c. Hence,

Read More: Equilateral Triangle

Perimeter of a Right Triangle

For a right-angle triangle i.e. the triangle with one angle of 90°. The perimeter is calculated by adding the length of all given sides. The formula to find the perimeter of a right triangle is:

where, 

a is the perpendicular, b is the base and c is the hypotenous of the right-angled triangle.

Read More: Right Angle Triangle

Related Article

• Pythagoras theorem
• Perimeter of Rectangle
• Circumference of circle
• Perimeter of Square
• Area of Triangle
• Sum of squares

Perimeter of a Triangle Examples

Example 1: If the length of the sides of a triangle is 4cm, 5cm, and 6cm, then what is the perimeter of the triangle?
Solution:

Given, the sides of the triangle are 4cm, 5cm, and 6cm. Thus, it is an scalene triangle.
So the perimeter of the triangle  = Sum of sides = 4 + 5 + 6 = 15cm

Example 2: What is the perimeter of an equilateral triangle whose one side length is 5cm?
Solution:

Given that the triangle is an equilateral triangle, thus all three sides are equal in length.

Since one side is equal to 5cm, the other two sides will also be equal to 5cm.
So, Perimeter = 5 + 5 + 5 = 15cm.

Example 3: Given the perimeter of an equilateral triangle is 21cm, find the length of its three sides.
Solution:

Since, in an equilateral triangle, all the three sides are equal in length, the perimeter is equal to three times the length of a side.
Let's the length of any side be equal to 'a' units. So perimeter is equal to '3a' units. So, we can write,

3a = 21
a = 7cm

Thus, the length of each side is equal to 7cm.

Example 4: Find the length of two equal sides of an isosceles triangle if the length of the unequal side is 5cm and the perimeter is 17cm.
Solution:

Given, the length of unequal side is 5cm and perimeter is 17cm.

Since, it is isosceles triangle, length of other two sides are equal. Let each equal side length be 'a' units.
Thus, perimeter = a + a + 5

Since, perimeter = 17cm, we can write,
17 = a + a + 5
2a + 5 = 17
2a = 12
a = 6cm

Thus, the length of the equal sides of the isosceles triangle is 6cm.