What is Perimeter? Definition, Formulas, Solved Examples

The word perimeter is derived from the Greek word ‘peri,’ meaning around, and ‘metron,’ which means measure. Perimeter is the closed path that outlines a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is known as circumference.

There are several applications where finding the perimeter is important. This could range from calculating the cost to fence the backyard garden to measuring the thread needed to mark the boundary of a soccer field. So let understand the concept of the perimeter in a better way.

Perimeter: Definition, Examples

The sum of the length of the boundary of a closed shape is called its perimeter. Let us try and understand this using an example.

Example 1: We have a huge farm that is square. Now, to save our farm from street animals, we decide to fence it. So, if we know the length of one side of the farm, multiply it by \(4\) to find the farm’s perimeter.

Example 2: If we need to find the length of the boundary of a square park, we must find its perimeter.

There are many such things, where we can find the perimeter.

Area and Perimeter

The area is the region or surface bounded by the shape of an object. The total space covered by a figure or a geometric shape is called its area. The area of a shape depends upon its dimensions and properties. Different shapes have different areas. For example, the area of a square is different from the area of a circle.

Area of a rectangular field \( = \) Length \( × \) Breadth

Units of area: In the CGS system, the unit of area is \({\rm{c}}{{\rm{m}}^2}\) and in the SI system, the unit of area is \({{\rm{m}}^{\rm{2}}}\).

The perimeter of a shape is defined as the total length around the shape. It is the length of a shape if it is expanded in a linear form.

Perimeter of the rectangular field \( = {\rm{ }}2\)(Length \( + \) Breadth)

What is the Perimeter of Triangle?

A triangle is a two-dimensional closed figure having three sides and three corners. The sum of the lengths of all sides is the perimeter of any polygon. In the case of a triangle, the perimeter of a triangle \(=\) Sum of the lengths of all three sides.

The perimeter of any closed shape is equal to the total length of its outer lines.

If a triangle has \(3\) sides a, b and c,

Perimeter of triangle \({\rm{(P) = a + b + c}}\)

What is the Perimeter of a Rectangle?

A quadrilateral which has two pairs of parallel and equal sides and all the four angles at the vertices are right angles, is called a rectangle.

The perimeter of a rectangle is the total length of its boundary.

Perimeter of a rectangle \(=\) Sum of all the four sides. If a is the length of two opposite sides and b is the breadth (width) of two opposing sides.

Then, the perimeter of rectangle \({\rm{(P) = a + a + b + b = 2(a + b)}}\)

What is the Perimeter of Square?

A square is a quadrilateral with four equal sides and all the four angles at the vertices are right angles. The perimeter of a square is defined as the length of its boundary.

Perimeter \(=\) Sum of the lengths of four sides \(=a+a+a+a=4 \times a\).

So, the perimeter of Square \({\rm{(P) = 4 a}}\) units, where a is the length of a side of the square.

What is the Perimeter of a Circle?

A circle is a closed two-dimensional circular figure with no corner and a center equidistant from any point on its boundary.

Perimeter of a circle is also called its circumference. It is the measurement of the boundary of the circle. If we open a circle and make a straight line out of it, then its length is the circumference of that circle.

When we use the formula to calculate the circumference of a circle, then the radius of the circle is required. So, we need to know the value of the radius \((r)\) or the diameter \((d = 2r)\) to evaluate the perimeter of the circle.

Now, perimeter/circumference of the circle \(= 2πr\), when radius \(r\) is known. \(=\pi d\), when the diameter \(d\) is known, where the value of \(\pi=\frac{22}{7}\) (approx.)

What is the Perimeter Formula?

The perimeter of any two-dimensional shape is equal to the sum of its sides. The formula to find the perimeter is given below:

Perimeter \(=\) Sum of all its sides

Let us summarise all the perimeter formulas in one table. It will be easy to remember.

How to find Perimeter of an Irregular Shape?

Perimeter \(=\) Sum of all its sides

To get the perimeter of the above figure, add the length of all its sides.

Thus, the perimeter \(=1 \mathrm{~cm}+1 \mathrm{~cm}+1 \mathrm{~cm}+1 \mathrm{~cm}+3 \mathrm{~cm}+3 \mathrm{~cm}+3 \mathrm{~cm}+3 \mathrm{~cm}\)
\(+2.5 \mathrm{~cm}+2.5 \mathrm{~cm}+2.5 \mathrm{~cm}+2.5 \mathrm{~cm}=26 \mathrm{~cm}\)

Therefore, the perimeter of the above figure is \(26 \mathrm{~cm}\).

Perimeter vs Area

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

We define area 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 centimetres, square metres, square feet, etc). Perimeter is measured in terms of the ‘number of’ units (centimetre, metre, feet etc).

Now, have a look at the image given below to understand what area and perimeter of any shape means,

Solved Examples – Perimeter

Q.1. If the length of the side of a square is \(12 \mathrm{~cm}\), Then find the total length of its boundary.
Ans: Given that the length of the side of a square \(=12 \mathrm{~cm}\). We know that the total length of the boundary is called the perimeter.
The perimeter of a square \(=4 \times\) side
So, the perimeter of the square \(=4 \times 12 \mathrm{~cm}=48 \mathrm{~cm}\)
Hence, the total length of the boundary is \(48 \mathrm{~cm}\).

Q.2. If the radius of a circle is \(28 \mathrm{~cm}\). Find its circumference.
Ans: Given the radius (r) of the circle \(=28 \mathrm{~cm}\).
The circumference of circle is called the perimeter of the circle.
We know that the circumference of a circle \(=2 \pi r\)
Now, the circumference of the circle \(=2 \times \frac{22}{7} \times 28 \mathrm{~cm}=176 \mathrm{~cm}\).
Hence, the circumference of the circle is \(176 \mathrm{~cm}\).

Q.3. Find the perimeter of a rectangle if its length is \({\rm{12\,m}}\) and breadth is \({\rm{7\,m}}\).
Ans: Given,
Length of the rectangle \({\rm{ = 12\,m}}\)
Breadth of the rectangle \({\rm{ = 7\,m}}\)
We know that the perimeter of rectangle \( = 2 \times ({\rm{ length }} + {\rm{ breadth }})\)
Now, the perimeter of the rectangle \( = 2 \times (12\;{\rm{m}} + 7\;{\rm{m}}) = 2 \times 19\;{\rm{m}} = 38\;{\rm{m}}\).
Hence, the perimeter of the rectangle is \({\rm{38\,m}}\).

Q.4. Find the perimeter of the below triangle.

Ans: Given that the three sides of the triangle are \(5 \mathrm{~cm}, 5 \mathrm{~cm}\) and \(3 \mathrm{~cm}\).
We know that perimeter is equal to the sum of all sides
Now, the perimeter of the triangle \(=5 \mathrm{~cm}+5 \mathrm{~cm}+4 \mathrm{~cm}=14 \mathrm{~cm}\)
Hence, the perimeter of the given triangle ABC is \(14 \mathrm{~cm}\).

Q.5. If the breadth of the rectangle is \(80\;{\rm{m}}\) and the perimeter is \({\rm{360\,m}}\). Find its length.
Ans: Given,
Breadth of the rectangle \({\rm{ = 80\,m}}\)
Perimeter of the rectangle \({\rm{ = 360\,m}}\)
Here, we need to find its length.
We know that,
Perimeter of the rectangle \( = 2 \times ({\rm{ Length }} + {\rm{ Breadth }})\)
\( \Rightarrow 360\;{\rm{m}} = 2 \times ({\rm{ Length }} + 80\;{\rm{m}})\)
\( \Rightarrow \frac{{360}}{2} = {\rm{ Length }} + 80\;{\rm{m}}\)
\( \Rightarrow 180 = {\rm{ Length }} + 80\;{\rm{m}}\)
\( \Rightarrow {\rm{ Length }} = 180\;{\rm{m}} – 80\;{\rm{m}} = 100\;{\rm{m}}\)
Hence, the length of the rectangle is \(100\;{\rm{m}}\).

Summary

This article helps to comprehensively learn how to calculate the perimeter of different kinds of geometric shapes like triangle, circle, rectangle, square depending on what information is available on the shapes. Knowing this, one can calculate the perimeter of any regular, irregular shape, land, etc.

Frequently Asked Questions (FAQ) – Perimeter

Q.1. What is the perimeter of ABCD?

Ans: Given

The length of the figure ABCD\(=4 \mathrm{~cm}\)
The breadth of the figure ABCD\(=2 \mathrm{~cm}\)
As the opposite sides of the plane’s closed surface are the same, it is a rectangle.
We know that the perimeter of the rectangle \( = 2({\rm{ length }} + {\rm{ breadth }})\).
So, the perimeter of rectangle \(ABCD=2\)\((4 \mathrm{~cm}+2 \mathrm{~cm})=2 \times 6 \mathrm{~cm}=12 \mathrm{~cm}\)
Hence, the perimeter of \(ABCD\) is \(12 \mathrm{~cm}\).

Q.2. What is the perimeter of shape B?

Ans: The given shape is,

We need to find the perimeter of the above shape.
Here, the length of one side (vertical line) \(=14 \mathrm{~cm}\)
The rest two parts of \(B\) is looking like a semi-circle. Two semi-circular parts of \(B\) make a circle.
Here, the diameter of the circle \( = \frac{{14}}{2} = 7\;{\rm{cm}}\)
Now, the radius \( = \frac{7}{2}\,{\rm{cm}}\)
As we know, the perimeter of a circle \( = 2\pi r = 2 \times \frac{{22}}{7} \times \frac{7}{2}\,{\rm{cm}} = 22\;{\rm{cm}}\)
Now, the perimeter of \(B=14 \mathrm{~cm}+22 \mathrm{~cm}=36 \mathrm{~cm}\)
Hence, the perimeter of the shape \(B\) is \(36 \mathrm{~cm}\)

Q.3. What is a perimeter in math?
Ans: Perimeter is the length around a plane or two-dimensional shape bounded by line segments or curves.

Q.4. How do I find the perimeter and area?
Ans: The perimeter is the length of the outline of any shape. The area is a measurement of the surface of a shape.
We use formulas to find the perimeter and area, where the shape is standard geometrical figures like, triangle, square, rectangle, circle etc.
When the figure is not a regular geometrical shape, we divide the given shape into a standard geometrical figure like triangle, square, rectangle, circle, etc. So, the standard formula can be applied.

Q.5.What is the formula for perimeter?
Ans: Perimeter of any shape \(=\) Sum of all its sides

Now that you are provided with all the necessary information about perimeter and perimeter formulas, we hope this article is helpful to you. If you have any queries on this page, post your comments in the comment box below and we will get back to you as soon as possible.

Happy Embibing!