106 LearnersLast updated on July 15th, 2025
Perimeter of Triangle
The perimeter of a shape is the total length of its boundary. The sum of all three sides is called the perimeter of a triangle. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a triangle.
What is the Perimeter of a Triangle?
The perimeter of a triangle is the total length of its three sides. By adding the length of all three sides, we get the perimeter of the shape.
The formula for perimeter of a triangle is π· = π + π + π, where a, b, and c are the sides of the triangle. For instance, if a triangle has sides, a = 6, b = 8, and c = 10, then its perimeter is p = 6 + 8 + 10 = 24.
Formula for Perimeter of Triangle - π· = π + π + π.
Let’s consider another example of a triangle with side lengths, π = 8, π = 10, and π = 12. So the perimeter of the triangle will be: π· = π + π + π = 8 + 10 + 12 = 30.
How to Calculate the Perimeter of Triangle
To find the perimeter of a triangle, we just need to apply the given formula and sum all the sides of the triangle.
For instance, a given triangle has the sides of a = 6, b = 6, c = 6. Perimeter = sum of all sides = 6 + 6 + 6 = 18 cm.
Example Problem on Perimeter of Triangle
For finding the perimeter of a triangle, we use the formula, π· = π + π + π.
For example, let’s say, a = 5 cm, b = 4 cm, and c = 2 cm. Now, the perimeter = sum of all sides = 5 + 4 + 2 = 11cm
Therefore, the perimeter of the triangle is 11 cm.
Tips and Tricks for Perimeter of Triangle
Learning some tips and tricks makes it easier for children to calculate the perimeter of triangles. Here are some tips and tricks given below:
- Always remember that a triangle's perimeter is simply the sum of the three sides of the shape. For that, use the formula, π· = π + π + π.
- Calculating the perimeter of a triangle starts by determining the length of each side using the distance formula. The distance formula is: Distance = √(x2-x1)2+(y2-y1)2 Here (x1, y1) and (x2, y2), Indicating the positions of two points that make out a triangle’s side. They can be found by adding the lengths of three sides after they are calculated.
- To reduce the confusion, specifically, arrange the indicated side lengths if you need the perimeter of a group of triangles. After that, apply the formula to each triangle.
- To avoid mistakes when adding the perimeter, make sure the side lengths are precise and constant for common uses like gardening and architecture.
- If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. Area-related calculations, like Heron’s formula, often use the semi-perimeter.
Common Mistakes and How to Avoid Them in Perimeter of Triangle
Did you know that while working with the perimeter of a triangle, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly using the Pythagorean theorem (a2 + b2 = c2) for triangles that are not right-angled.
Remember that only right-angled triangles can use the Pythagorean theorem. The lengths of all the sides of other triangle types should be summed up to find the perimeter.
Mistake 2
Students may confuse the concepts of area and perimeter, leading to incorrect calculations.
It is important to note that the perimeter, calculated in linear units, is the total length of the triangle’s sides, while the area, in square units, represents the space inside the triangle.
Mistake 3
Assuming that every triangle is isosceles or equilateral, which results in inaccurate calculations.
A scalene triangle has all the sides of different lengths. Always be careful about the type of the triangle’s type to ensure accurate calculations.
Mistake 4
Using the wrong values for the length of the sides, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct lengths for your triangle.
Mistake 5
Misunderstanding or misidentifying the side lengths that are given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if it's possible, try to draw a triangle to accurately identify the side lengths.
Perimeter of Triangle Examples
Problem 1
A triangular-shaped road sign has a perimeter of 48 inches and two sides, the two sides measuring 17 inches each. To find out the missing side of the road, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 14 inches.
Explanation
Let ‘b’ be the side of the missing side.
And the given perimeter = 48 inches.
Length of the two equal sides = 17 inches.
Perimeter of triangle = sum of lengths of three sides.
48 = 17 + 17 + b
48 = 34 + b
b = 48 – 34 = 14
b = 14
Therefore, the missing side is 14 inches.
Problem 2
A wire with a perimeter of 297 inches is reshaped into an equilateral triangle. Find the length of each side of the triangle and divide the total length by 3.
99 inches
Explanation
Given that the perimeter of a rectangle is equal to the total length of the wire and this wire is reshaped into an equilateral triangle, here is the solution:
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
297 ÷ 3 = 99
a = 99
Therefore, the length of each side of the triangle is 99 inches.
Problem 3
Find the perimeter of an equilateral triangle whose sides are 10cm.
30 cm
Explanation
Perimeter of triangle = a + b + c
P = 10 + 10 + 10 = 30
Therefore, the perimeter of the triangle is 30 cm.
Problem 4
Annie is planning a triangular vegetable garden in her backyard. She measures the three sides of the garden: Side A = 12 meters Side B = 9 meters Side C = 15 meters How much string should Annie buy to go around the edge of the garden?
Annie will need 36 meters of string to go around the garden.
Explanation
The perimeter of a triangle is the sum of all the three sides. Using the formula:
P = a + b + c
P = 12 + 9 + 15 = 36 meters.
Problem 5
Find the perimeter of the scalene triangular rock.
Sides are a = 10, b = 8, c = 7
Perimeter = a + b + c
= 10 + 8 + 7 = 25 meters.
Explanation
Each side of the scalene triangle has a different length. The entire distance is calculated around the rock to be 25 meters by summing the lengths of the three sides.
FAQs on Perimeter of Triangle
1.Evaluate the triangleβs perimeter if its sides are 3cm, 4cm, and 6cm.
2.What is meant by a triangleβs perimeter?
3.What are the types of triangles?
4.Which triangle has no equal sides?
5. Which triangle has the smallest perimeter?
Important Glossaries for Perimeter of Triangle
- Perimeter: The total length of the sides of a shape.
- Triangle: A polygon with three sides and three angles.
- Formula of perimeter: The mathematical expression used to calculate the perimeter of a triangle is π· = π + π + π.
