Perimeter of a Triangle
Perimeter of a triangle is defined as the total length of the boundary of the shape. A triangle is a polygon having 3 vertices and 3 sides. Triangle can be classified into different types based on the measures of lengths and angles. Different formulas and methods can be used to calculate the perimeter of a triangle based on the type of triangle. We will learn about these different formulas and methods using solved examples in the following sections.
1.  Perimeter of a Triangle 
2.  Perimeter of a Triangle Formula 
3.  How To Find the Perimeter of Triangle? 
4.  FAQs on Perimeter of Triangle 
Perimeter of a Triangle
The perimeter of a triangle means the sum of its boundary or all three sides. The word perimeter is a combination of two Greek words – “peri” which means around and “metron” meaning measure. The total distance around any twodimensional figure is defined as its perimeter. Since perimeter gives the length of the boundary of a shape, it is given in units.
Reallife example: Imagine that we need to fence the triangular park. Now, to know the dimensions of the fence, we add the lengths of the three sides of the park. This length or distance of the boundary of a triangle is called the perimeter of the triangle.
Perimeter of a Triangle Formula
To calculate the perimeter of a triangle, we simply add the lengths of the sides given. We use different formulas to calculate the perimeter of a triangle based on the type of triangle. The general formula used to calculate the perimeter of a triangle is :
Perimeter = sum of the three sides
Let us understand this formula with the different types of triangles.
Perimeter of a Scalene Triangle
If a triangle has all three sides of different lengths, it is a scalene triangle. The perimeter of a scalene triangle can be calculated by finding the sum of all the unequal sides. The formula for the perimeter of a scalene triangle is: Perimeter = a + b + c, where "a", "b", and "c" are the three different sides.
Perimeter of an Isosceles Triangle
If a triangle has two sides of equal length, it is an isosceles triangle. The perimeter of an isosceles triangle can be calculated by finding the sum of the equal and unequal sides. The formula for the perimeter of an isosceles triangle is: Perimeter of an isosceles triangle = 2a + b
where,
 a = sides of equal length
 b = the third side
Perimeter of an Equilateral Triangle
An equilateral triangle has all the sides of equal measure. The formula for the perimeter of an equilateral triangle is:
Perimeter of an equilateral triangle = 3 × a
where 'a' = length of each side of the triangle.
Perimeter of a Right Triangle
A triangle having one of the angles of the measure of 90º is called a rightangled triangle. The perimeter of a right triangle can be calculated by adding the given sides. The formula to calculate the perimeter of a right triangle is given as,
Perimeter of right triangle, P = p + b + h
We know, using Pythagorean theorem, h^{2 }= p^{2} + b^{2}
Therefore, P = p + b + √(p^{2} + b^{2})
where,
 h = Hypotenuse of right triangle
 p = Perpendicular of right triangle
 b = Base of right triangle
Perimeter of Right Isosceles Triangle
A right triangle with equal sides and two angles equal is called a right isosceles triangle. The perimeter of an isosceles right triangle can be calculated by adding the given sides. The formula to calculate the perimeter of a right isosceles triangle is given as,
Perimeter of right isosceles triangle, P = h + 2l
Using the Pythagorean theorem, we know, h = √(l^{2}+ l^{2}) = √2 × l
or, l = h/√2
Therefore, P = 2l + (√2)l = (2 + √2)l units
Also, P = h + 2(h/√2) = h + √2 × h units
How to Find The Perimeter of a Triangle?
The perimeter of a triangle cal be calculated by following the steps given below,
 Step 1: Note the measurements of all the sides of a triangle and check that all the sides should have the same unit.
 Step 2: Calculate the sum of all the sides.
 Step 3: Represent the answer along with the unit.
Let us see how to find the perimeter of a given triangle using an example.
Example: Find the perimeter of △ABC having the following dimensions:
AB = 6 inches, BC = 8 inches, AC = 10 inches
Solution:
Step 1: Check if all three sides of the triangle are known.
AB = 6 inches, BC = 8 inches, AC = 10 inches
Step 2: Use the appropriate formula and add the sides to get the perimeter.
Since this is a scalene triangle, we use the formula:
Perimeter = a + b + c
Write the perimeter along with its units.
Perimeter of triangle ABC = 6 + 8 + 10 = 24 inches.
Important Notes:
 All the sides of a scalene triangle are of different lengths.
 An isosceles triangle has two sides of equal lengths and the third side of a different length.
 An equilateral triangle has all its sides of equal lengths.
Solved Examples on Perimeter of a Triangle

Example 1: Find the perimeter of a right triangle PQR with sides PQ = 4 inches, QR = 3 inches, and where side PR (the hypotenuse) is not known.
Solution:
Given, PQ = 4 inches, QR = 3 inches, PR = ?
To calculate the perimeter of the triangle, we need to know all three sides.
Since here we need to calculate the perimeter of a right triangle, we will use the Pythagorean theorem.
PR² = PQ² + QR²
PR² = 4² + 3²
PR² = 16 + 9
Therefore, PR = √25
PR = 5 inches.
Now, we can calculate the perimeter of the triangle.
Perimeter of triangle PQR = Sum of the three sides
= 3 + 4 + 5 = 12
Therefore, the perimeter is 12 inches.
Answer: Perimeter of the triangle = 12 inches

Example 2: Find the length of the missing side of a triangularshaped road sign whose perimeter is 48 inches and the two sides are 17 inches each.
Solution:
Given, Perimeter = 48 inches.
Length of the two equal sides = 17 inches.
So, this shows that it is an isosceles triangle.
Perimeter of an isosceles triangle = 2a + b
48 = (2 × 17) + b
48 = 34 + b
b = 14
Therefore, b = 14 inches
Answer: Length of the missing side = 14 inches.

Example 3: The perimeter of a rectangular wire is 297 inches. The same wire is bent into the shape of an equilateral triangle. Find the length of its each side.
Solution:
We know that, perimeter of a rectangle = total length of the wire
Length of the wire used = Perimeter of the triangle formed
Perimeter of an equilateral triangle = 3 × a
297 =3 × a
a = 99
Answer: The length of each side of the triangle = 99 inches
FAQs on Perimeter of Triangle
What Is the Perimeter of a Triangle?
The perimeter of a triangle is defined as the total length of the boundary of the shape. The total distance around any twodimensional figure is the perimeter of the given shape.
What Is a Formula of Perimeter of Triangle?
The perimeter of a triangle can be calculated by simply adding the length of all the sides. The general formula to calculate the perimeter of a triangle with sides 'a', 'b', and 'c' is given as: a + b + c units.
How Do You Find the Perimeter of a Triangle With Three Equal Sides?
To calculate the perimeter of the triangle with three equal sides, we add the length of all sides, or multiply the length of any one side by 3. We refer to this type of triangle as an equilateral triangle. The formula to calculate the perimeter of an equilateral triangle is 3a, where 'a' is the length of each side.
Can a Triangle Have the Same Area and Perimeter?
A triangle can have an equal perimeter and area for only some special cases. These shapes having an equal perimeter and area are called equable shapes. Thus, a triangle with an equal perimeter and area is called an equable triangle.
How Do You Find the Third Side and Perimeter of a Right Triangle Given Two Sides?
The third side of a triangle can be calculated using the measure of the other two sides, by applying the Pythagorean theorem. According to the Pythagorean theorem, for any righttriangle with sides 'p', 'b', and 'h',
h^{2 }= p^{2} + b^{2}
where,
 h = Hypotenuse of right triangle
 p = Perpendicular of right triangle
 b = Base of right triangle
the perimeter for the triangle is p + b + h units.
How Do You Find the Perimeter of a Triangle With Coordinates?
The lengths of the sides of a triangle, given the coordinates, can be calculated using the distance formula. Once, these lengths are obtained, we can simply add them to find the perimeter of the given triangle.
What Is the Difference Between the Area and Perimeter of a Shape?
The perimeter of a shape is the total path that encompasses or surrounds a shape, while the area is the total region or space covered by the shape. The perimeter of a shape is represented in units, whereas we use (unit^{2}) or sq unit to represent the area.
How Do You Find the Perimeter of a Triangle With Two Equal Sides?
To calculate the perimeter of the triangle with two equal sides, we find the sum of length of all sides. We refer to this type of triangle as an isosceles triangle. The formula to calculate perimeter of an isosceles triangle is: 2a + b, where 'a' is the length of equal side, and 'b' is the length of the third side.