The Perimeter of Rectangle Formula

The Perimeter of Rectangle Equation

We come across many shapes whose distance around has to be calculated and this is termed as the perimeter of the shapes. We see many shapes around like square, rectangle, circle, polygon, etc. Every shape has its unique properties and measurements. Hence every shape has a different perimeter, based on their measurements. A perimeter is the length of the boundary enclosed by any geometric shape. The perimeter of the shape depends on the length of the shape. For example, a metal wire of length 10 cm can form both the circle and the square.


Suppose you have to fence your house, the length required for fencing is the perimeter of the house. Perimeters of two shapes can be equal only if their length is equal.


In this article, we will study what is a rectangle and perimeter of rectangle formula example.


Perimeter of Rectangle Formula = 2 x (length + breadth)


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What is a Rectangle?

A rectangle is a quadrilateral having four sides. The opposite sides of a rectangle are parallel and of equal length. Since a rectangle has four sides, it has four angles.


All angles of a rectangle are equal. It is an equiangular rectangle with four right angles which is 90 degrees. Another property of the rectangle is that it two diagonals of equal length. Diagonals are a line that is drawn inside the rectangle connecting opposite corners or vertices and hence the diagonals of a rectangle are congruent.


When we go round a closed figure or body, along its boundary, for once, we cover a distance. The measure of the distance is the perimeter of the figure or body. To understand and measure the perimeter of the rectangular field, we travel along the boundary of the four sides of the field, starting from a point and ending at the same point. While doing so, we observe that we measure the length and breadth, both, twice.


Some of the examples of rectangles are cement blocks, picture frames, posters, sheets of paper, the faces of play bricks that snap together, the sides of shoe boxes and cereal boxes, and a lot of other everyday objects.


Properties of a Rectangle

  • It is a flat shape.

  • It has 4 sides (edges).

  • It has 4 corners (vertices).

  • It has 4 right angles.

 

Perimeter of Rectangle

A four-sided polygon having two dimensions i.e. length and breadth is called a rectangle. To calculate the perimeter of the rectangle we have to add all the four sides of the rectangle.


In a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the height of the rectangle.


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Perimeter of rectangle formula = sum of all the four sides

= length + width + length + width

= 2 length + 2 width

Perimeter of rectangle formula =   2 × (length + width)


Perimeter of rectangle formula =   2 × (length + width) = 2( l + b )


Area of Rectangle

Area = length × width


Diagonals of a Rectangle

A rectangle has two diagonals, they are equal in length and intersect in the middle. A diagonal's length is the square root of (length2 + width2):


Diagonal 'd' = √(a2 + b2)


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\[\text{Diagonal of Rectangle} = \sqrt{(length^{2} + width^{2}})\]


Perimeter Formula Chart  for Different Shapes

Here is the list of formulas for the perimeter of different shapes.


Formula of Perimeter Shapes

Name of Geometric Shapes

Figure

Perimeter Formula

Variables

Rectangle

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Perimeter of rectangle =

2(l +w)

l =  length

w  = width

Square

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Perimeter of square = 4a

a = sides of the square

Triangle

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Perimeter of triangle = sum of all sides

b = base

h = height

Trapezoid

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Perimeter of trapezoid = Sum of all sides.

a =base 1

b = base 2

h = vertical height

Parallelogram

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Perimeter of parallelogram = 2(a+b)

a = side

b=base

h=vertical height


Rhombus

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Perimeter of rhombus = 4a

a = side of rhombus

h = height

Circle

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Perimeter of circle/Circumference  = 2πr

r = radius of the circle

π = 22/7 or 3.1416

Semicircle

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Perimeter of semicircle = πr + 2r

r = radius of the circle

Sector

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Perimeter(sector) = 2(radius) + arc length

r = radius of the circle


Solved Examples

The perimeter of rectangle formula example


Example 1:

Find the perimeter of a rectangle whose length and breadth are 11cm and 13cm, respectively.


Solution:

Given that length = 11 cm and Breadth = 13cm

We have,

The perimeter of rectangle formula  = 2( length + breadth)

Perimeter, P = 2(11 + 13) 

P = 2 x 24 cm

P = 56 cm

Therefore, the perimeter of a rectangle is 56 cm.


Example 2:

The length of the rectangular field is 15m and the width is 6m. Find the perimeter of a rectangle field and also find the area.


Solution:

Given that   Length = 15m

Width = 6m

We have,  Area formula A = length x width 

= 15 x 6 

= 90 m2

formula to calculate perimeter of rectangle P = 2 (length + width) 

= 2 x (15 + 6) 

= 2 x 21

= 42 m.


Quiz Time

Example 1. If the perimeter of the given rectangle is 8 cm and the length of one of its sides is 2 cm. What will be the other side?


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Example 2. A rectangular playground is 21 m long and 15 m wide. Find its perimeter.


Fun Facts

Many historical buildings are rectangular in shape e.g. Parthenon in Athens.

FAQ (Frequently Asked Questions)

1. What is the Difference Between Area and Perimeter?

Answer: Key differences between area and perimeter are :


The area is the region occupied by the two-dimensional object.

Perimeter is the length of the boundary enclosed by the geometric figure.

The area is the inner space of an object.

Perimeter is the length of the outer boundary of an object.

The area represents a two-dimensional object so  is measured in square units.

Perimeter represents a dimensional object so it is measured in linear units.

Example: Space covered by a garden.

Example: Length of the boundary of the garden.

2. Where do we use Perimeter in Daily Life?

Answer: Uses of the perimeter in daily life are as follows:

  • The perimeter of a plot is calculated for constructing buildings.

  • Perimeter is required for fencing the compound walls.

  • Perimeter is needed to sew edges of a quilt.

  • Perimeter is required to paste a decorative tape around the greeting card.