# Perimeter

Go back to  'Mensuration and Measurement'

## Introduction to Perimeter

Let’s say there is a park in your housing society. If the residents' welfare association wishes to calculate the amount of grass that needs to be mown in the lawn inside the park, then the area needs to be calculated. But if the association is planning to erect a fence around the lawn, then the perimeter of the lawn needs to be calculated to find out the length of fencing required. An area is some two dimensions, but a perimeter is just a measure of length and is a one-dimensional number.

## The Big Idea: What is perimeter?

A perimeter of a closed space is the sum of the length of the bounding sides of the space.

As you must have understood by now, a perimeter is simply a total of the dimensions of the sides that bound a closed space. You can add up the sides of a closed space to get the perimeter, but for some of the standard shapes, we also have formulas to calculate the perimeter easily.

## How is it important?

### The perimeter of a triangle

If the three sides of a triangle are represented by the letters $${a,\;b,\text{ and }c}$$, then the $${\text{perimeter of the triangle} = a + b + c}$$, and you must take care to ensure that all the three sides of the triangle are in the same units.

### The perimeter of a rectangle

We know that in a rectangle, four sides are bounding this four-sided figure. Of the four sides, the opposite two are equal. So, if the opposite sides of a rectangle are termed ‘$${a}$$' and ‘$${b}$$' respectively, then the perimeter of the rectangle can be calculated as

\begin{align}\text{Perimeter of rectangle} = a + b + a + b = 2a + 2b = 2\left( {a + b} \right)\end{align}

### The perimeter of a square

The only difference between a square and a rectangle is that a rectangle has both sets of opposite sides equal, instead of all four sides being equal. When we are dealing with a square, we do not need to deal with two sets of lengths, but a single side, say ‘$${s}$$'. To calculate the perimeter with side ‘$${s}$$', we can represent it as

\begin{align}\text{Perimeter of square} = s + s + s + s = 4s\end{align}

### The perimeter of a quadrilateral

A quadrilateral is just a closed space with all sides of different lengths, and all internal angles have different values. That is why when you need to calculate the perimeter of a quadrilateral you add up the value of the four sides. There is no easy formula to use.

### The perimeter of a parallelogram

A parallelogram is a quadrilateral with opposite pairs of sides being parallel and also equal. So, the formula for finding the perimeter of a parallelogram with opposite sides represented by ‘$${a}$$’ and ‘$${b}$$’ respectively can be represented as

\begin{align}\text{Perimeter of parallelogram} = a + b + a + b = 2a + 2b = 2\left( {a + b} \right)\end{align}

### Perimeter vs Area

Many of us get confused between what the perimeter and area of a closed space is. One easy way to remember this is to remember that the word perimeter has the word ‘Rim’, and rim stands for the outer boundary of any shape. So, when you are dealing with the length of the ‘rim’ of a closed space, then you need to find its perimeter.

In this chapter, we only learn about the perimeter of closed figures made by three or more straight lines. Subsequently, we will also learn about the perimeter and area of a circular shape like a circle. That will not involve the addition of any lengths of the figure but just a simple formula using the radius of the circle.