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126 LearnersLast updated on December 11, 2025
Perimeter of Length
The perimeter of a shape is the total length of its boundary. It is often used in scenarios such as fencing a property, sewing, and more. In this topic, we will learn about the perimeter of various shapes in terms of their lengths.
What is the Perimeter of Length?
The perimeter of a shape is the total length of its boundary.
By adding the lengths of all the sides, we get the perimeter of the shape.
For example, if you have a rectangle with sides measuring 8 cm and 5 cm, its perimeter is P = 2(8 + 5) = 26 cm.
Formula for Perimeter of Length
Consider a rectangle with side lengths, a = 8 cm, and b = 5 cm.
The formula for the perimeter is P = 2(a + b).
So the perimeter of the rectangle will be: P = 2(a + b) = 2(8 + 5) = 26 cm.
How to Calculate the Perimeter of Length
To find the perimeter of a shape, apply the given formula and sum all the side lengths.
For instance, for a square with sides of 6 cm, the perimeter is 4 times the side length = 4 * 6 = 24 cm.
Example Problem: For a rectangle, use the formula, P = 2(a + b).
For example, let’s say, a = 5 cm, b = 4 cm. Now, the perimeter = 2(5 + 4) = 18 cm. Therefore, the perimeter is 18 cm.
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Tips and Tricks for Perimeter of Length
Here are some tips and tricks to easily calculate the perimeter of shapes:
Always remember that a shape's perimeter is simply the sum of its side lengths.
For rectangles, use the formula, P = 2(a + b).
Calculating the perimeter starts by determining the length of each side.
For irregular shapes, break them into known shapes, calculate their perimeters, and sum them up.
To reduce confusion, arrange the side lengths logically if you're dealing with multiple shapes.
For precise uses like construction or landscaping, ensure side lengths are measured accurately.
If given the semi-perimeter (half of the perimeter), multiply it by 2 to find the total perimeter.
This concept is often applied in calculations involving triangles.
Common Mistakes and How to Avoid Them in Perimeter of Length
While calculating the perimeter, some common errors may occur.
Here are solutions to help avoid them:
Mistake 1
Using area formulas instead of perimeter formulas.
Remember that the perimeter is a linear measure, not an area.
Always use the correct formula for the shape's perimeter.
Mistake 2
Confusing side lengths in different units.
Ensure all side lengths are in the same unit before calculating the perimeter.
Convert units if necessary to maintain consistency.
Mistake 3
Assuming all sides are equal in irregular shapes.
For shapes like scalene triangles or irregular polygons, check each side length individually to ensure accurate calculations.
Mistake 4
Misreading side lengths or using incorrect values.
Double-check the given measurements and use the correct values for your calculations.
Mistake 5
Misidentifying the shape type.
Before starting calculations, confirm the shape type and use the appropriate formula for its perimeter.
Perimeter of Length Examples
Problem 1
A rectangular garden has a perimeter of 48 meters and two sides measuring 17 meters each. Find the missing side length.
Length of the missing side = 7 meters.
Explanation
Let ‘b’ be the missing side length.
Given perimeter = 48 meters.
Two known sides = 17 meters each.
Perimeter of rectangle = 2(a + b).
48 = 2(17 + b)
48 = 34 + 2b
2b = 48 – 34
2b = 14
b = 7
Therefore, the missing side is 7 meters.
Problem 2
A wire with a perimeter of 297 inches is reshaped into a square. Find the length of each side of the square.
74.25 inches
Explanation
Given that the perimeter of the wire is the same as the perimeter of the square, here is the solution:
Perimeter of square = 4 × a 297 = 4 × a 297 ÷ 4 = 74.25 a = 74.25
Therefore, the length of each side of the square is 74.25 inches.
Problem 3
Find the perimeter of a square whose side is 10 cm.
40 cm
Explanation
Perimeter of square = 4 × side length P = 4 × 10 = 40
Therefore, the perimeter is 40 cm.
Problem 4
A picture frame has sides measuring 12 cm and 9 cm. How much ribbon is needed to go around the frame?
42 cm of ribbon is needed.
Explanation
The perimeter of a rectangle is the sum of all the sides.
Using the formula: P = 2(a + b)
P = 2(12 + 9) = 42 cm.
Problem 5
Find the perimeter of an irregular polygon with side lengths of 10 m, 8 m, 7 m, and 5 m.
The perimeter is 30 meters.
Explanation
Add up all the side lengths to find the total perimeter: 10 + 8 + 7 + 5 = 30 meters.
FAQs on Perimeter of Length
1.Evaluate the perimeter of a rectangle if its sides are 3 cm and 4 cm.
2.What is meant by a shape's perimeter?
3.What are common shapes used in perimeter calculations?
4.Which shape has no equal sides?
5.Which shape has the smallest perimeter for a given area?
Important Glossaries for Perimeter of Length
- Perimeter: The total length of the sides of a shape.
- Rectangle: A polygon with four sides and opposite sides equal.
- Square: A polygon with four equal sides and four equal angles.
- Scalene Triangle: A triangle with all sides of different lengths.
- Polygon: A closed shape with multiple straight sides.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
