Perimeter of Rectangle

Perimeter of Rectangle could be considered as one of the characteristics or properties of the rectangle. It is the total distance covered by the rectangle. In Maths, you will come across many geometric shapes and sizes, which has an area, perimeter and even volume(for 3-d figures). You will also learn the formulas for all those parameters. Some of the examples of different shapes are circle, square, polygon, quadrilateral, etc. In this article, we will study the key feature of the rectangle, i.e. perimeter.

Perimeter basically gives the length of the figure. Suppose for a square, which has all its sides as equal, the perimeter of the square will be four times of its sides. In case of a circle, the perimeter is termed as circumference, which is calculated based on its radius. Before we find out the perimeter of a given rectangle, let us learn first, what a rectangle is.

Rectangle Definition

A Rectangle is a quadrilateral which has four sides, having all the internal angles to be right-angled (90°). It has length and width, which are unequal to each other. The opposite sides are equal in length and parallel to each other, unlike the square, which has all its sides equal.

Rectangle

Perimeter of a Rectangle Formula

Now as we have already discussed about rectangle and its properties, let us derive the formula for its perimeter and area.

Suppose a rectangle has length and width as b and a respectively.

Perimeter of rectangle formula

From the definition of the perimeter we know,

The perimeter of a rectangle = sum of all its sides

= a+b+a+b

=2(a+b)

Therefore,

Perimeter of a rectangle = 2(Length + Width) square unit

 

Now let us write the formula for the area of a rectangle, with respect to same above given figure;

Area of a rectangle = Length × Width = a × b

Example Problems

Q.1: Find the perimeter of a rectangle whose length and width is 5 cm and 10 cm, respectively?

Solution: Given:

Length = 5 cm and Width = 10cm

We know,

The perimeter of a rectangle = 2(length + width)

Substitute the value of length and width here,

Perimeter, P = 2(5 + 10) cm

P = 2 x 15 cm

Therefore, the perimeter of a rectangle = 30 cm

Q.2: Find the perimeter of a rectangle whose length and breadth are 12cm and 15cm, respectively.

Solution:

Given:

Length = 12 cm and Breadth = 15cm

We know,

The perimeter of a rectangle = 2(length + width)

Substitute the value of length and width here,

Perimeter, P = 2(12 + 15) cm

P = 2 x 27 cm

Therefore, the perimeter of a rectangle = 54 cm

Q.3: A rectangular yard has length equals to 10cm and perimeter equals to 60. Find its width.

Solution: Given,

Perimeter of the yard = 60cm

Length of the yard = 10cm

From the formula, we know,

Perimeter, P = 2(length + width)

Putting the values, w get;

60 = 2(10 + width)

10 + W = 30

W = 30-10=20

Hence, the width of the yard is 20cm.

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Practice Questions

  1. Find the perimeter of a given rectangle which has length=15cm and width=20cm.
  2. What is the length of the rectangular field which has a perimeter of 100cm and width of 25cm?

Frequently Asked Questions

What is the area and perimeter of a rectangle?

The area of a rectangle can be defined as the region that the rectangle covers in a two-dimensional space. The area of a rectangle can also be defined as the number of square units it takes to completely fill the rectangle.

The perimeter of a rectangle is defined as the total distance around the outside of a rectangle. In simple words, a rectangle’s perimeter is the total boundary of it.

How to find the perimeter of a rectangle?

To get the perimeter of a rectangle, add all the sides of it. There are 4 sides of a rectangle whose sum will give its perimeter.

What is the formula for the perimeter of a rectangle?

The formula for the perimeter of a rectangle is, P = length+breadth+length+breadth.

Or, P = 2(length+breadth)

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