Perimeter

The outer boundary that make up a geometrical shape is called its perimeter. However, in the case of a circle, it is called a circumference. How does one calculate the perimeter?

Square-shaped park

In this chapter, you will learn the perimeter formulae for various geometric shapes. Once you get the hang of the basics, you will be able to solve our perimeter examples at the end of this chapter.

Check out the interactive examples to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page.. 

Lesson Plan 

What is Perimeter?

Perimeter Definition

The perimeter of a shape is defined as the total distance around the shape.

It is the length of any shape that can be expanded in a linear form.

The perimeter of different figures can be equal in length depending upon the dimensions.

Garden image with kids, showing boundary and representing perimeter

For example, imagine a triangle made of wire of length L, the same wire can be reuse to make a square, considering all the sides are equal in length.

Example of a wire used to frame triangle and square to show equal perimeter.


What is the Formula For Perimeter?

Perimeter Formula

Look at the image below with measuring dimensions as 1 in.

Square chocolate piece with dimensions 1 inch each

The perimeter of any 2-dimensional figures is measured as the sum of its all the sides.

Hence, the perimeter of a given square-shaped chocolate piece is \(\ 1+1+1+1=4\ in\)

The perimeter formula is,

 Perimeter = Sum of all the sides.

The perimeter formula for different 2-D figures is shown in the table below:

PERIMETER FORMULAS

Square with side L The perimeter of a square=\(\ 4\times L\)
L = length of a side.

Rectangle ABCD with sides p and q

The perimeter of a rectangle=\(\ 2\times(p + q)\)

Triangle PQR with sides a, b, and c

The perimeter of a triangle=\(\ a + b + c\)

Quadrilateral ABCD with a, b, c, and d as sides

The perimeter of a quadrilateral=\(\ a + b + c + d\)

Circle with radius r.

The perimeter of a circle=\(\ 2 \pi r\)
r = radius

What is Area? 

The word "area" means vacant surface in Latin.

The area can be defined as the amount of space covered by a flat surface of a particular shape.

It is measured in terms of the "number of" square units (square yards, square inches, square feet, etc.).

Most objects or shapes have edges and corners.

The length and breadth of these edges are considered while calculating the area of a specific shape.

For example, 

Square tile with sides and showing area of square

The area is the space occupied by shape whereas the perimeter is the total distance covered around the edge of the shape.

 
Thinking out of the box
Think Tank
  1. Think about the difference between perimeter and area of a 2-dimensional shape.
  2. Think about any figure with 8 sides and try to find its perimeter.

How To Find Perimeter?

Let us consider one perimeter example.

David wants to put a fence around his farm so that his sheep will not wander away. 

He wants to know how much wire he would need to put a fence around his rectangular farm.

Rectangular shape farm.

Let us first name the sides of his farm.

The larger side of this rectangular farm is named \(l.\)

The smaller side is named \(b.\)

Now, if we add the distance of all 4 sides of his farm, it will give us the perimeter.

Total distance = \(\ l+b+l+b = 2l + 2b\) 

Therefore,

\[\text{Perimeter of a Rectangle} = 2(l+b)\]

Perimeter Calculator

Try to find the perimeter of 2-D shapes using a perimeter calculator.


Solved Examples

Let us look at some solved perimeter examples to understand the topic logically.

Example 1

 

 

Your favorite chocolate bar is made up of equal-sized squares with each side measuring 1 in.

Calculate its perimeter.

Rectangular Chocolate bar with dimensions 1 in

Solution

We know that each little square has all its sides = 1 in.

If we count and add the sides of squares along the length of the bar, we get 3 in.

The sides of squares along the breadth of the bar add up to 2 in.

Therefore, the length of the bar = 3 in.

The breadth of the bar = 2 in.

Chocolate piece with dimensions

\[\begin{align}\text{Perimeter} &=2(l+b)\\\ &=2(3+2)\\\ &= 2(5)\\\ &=10\ in\end{align}\]

\(\therefore\) The perimeter of the chocolate bar is 10 in.
Example 2

 

 

Joseph has five square-shaped photo frames. Each frame is equal in size. Calculate the perimeter.

Sqaure-shaped photo frames

Solution

We know that each square frame has all its sides = 3 in

Total frames = 5

\[\begin{align}\text{Perimeter of 1 square frame} &=4(L)\\\ &=4(3)\\\ &=12\ in\\\text{Perimeter of 5 frames} &=5\times12\ in\\\ &= 60\ in\end{align}\]

\(\therefore\) Perimeter of 5 frames is 60 in.
 
Challenge your math skills
Challenging Questions

1. Find the perimeter of a quadrilateral with adjacent sides as 3 in and 4 in.
2. Find the perimeter of a triangle with sides as 4 in, 5 in, and 6 in.
3. Find the perimeter of a circle with a radius of 3.5 in.  

Interactive Questions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

 

 
 
 
 
 

Let's Summarize

We hope you enjoyed learning about perimeter with the simulations, practice questions, and perimeter examples. Now you will be able to easily solve problems on perimeter using perimeter calculator, perimeter formula, and perimeter definition.

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Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


Frequently Asked Questions (FAQs)

1. What is the perimeter in feet?

Let us find the perimeter in feet of a square. Consider a square of a side 4 ft. The perimeter of a square is \(\ 4\times(side)\).

\(\text{Perimeter}=4\times4= 16\ ft.\). 

2. What is the perimeter of a table?

Consider a rectangular table with length 30 in and breadth 25 in.

Therefore, the length of the table = 30 in.

The breadth of the table = 25 in.

\(\begin{align}\text{Perimeter} &=2(l+b)\\\ &=2(30+25)\\\ &= 2(55)\\\ &=110\ in\end{align}\)

3. Where do we use perimeter in real life?

Perimeter is very useful in real life and plays a crucial role. If you are planning to construct a house then an accurate perimeter is required of doors, windows, roof, walls, etc.

  
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
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