Area of Rectangle

Area of Rectangle

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Introduction to Area

The area of any shape is the number of unit squares that can fit into it.

What is a unit square?

A unit square is a square of side \(1\) unit. 

Introduction to area of a rectangle: a unit square is a square of 1 unit side length.

Here "unit" can refer to any unit such as centimeter, meter, kilometer, etc.

Let us do a small activity to understand about area using unit squares.

Let's find the area of some shapes by placing them on a grid paper of unit squares and counting the number of unit squares inside the shape.

The area of any shape is measured in square units such as \(\text{cm}^2\), \(\text{m}^2\), \(\text{km}^2\) etc depending on the given unit.

If no unit is given, the unit of area is considered to be "square units".

Introduction to area of a rectangle : areas of some shapes are found by counting the number of unit squares.

Introduction to area of a rectangle : areas of some shapes are found by counting the number of unit squares.

Introduction to area of a rectangle : areas of some shapes are found by counting the number of unit squares.

Introduction to area of a rectangle : areas of some shapes are found by counting the number of unit squares.

We will find the area of a rectangle in a similar way.


Definition of Area of a Rectangle

As discussed above, the area of a rectangle is the number of unit squares that can fit into it.

For example, let us consider a rectangle of length 4 cm and breadth 3 cm.

Area of a rectangle of length 4 cm and breadth 3 cm using unit squares

Let us draw unit squares inside the rectangle.

Each unit square is a square of length 1 cm.

Area of a rectangle of length 4 cm and breadth 3 cm using unit squares

Now, count the number of unit squares in the above figure.

How many squares can you observe?

There are 12 squares in total.

We have already learnt that area is measured in square units.

Since the unit of this rectangle is "centimeters", the area is measured in square centimeters which can also be written as \(\text{cm}^2\).

Thus,

Area of the above rectangle = \({12\text{ cm}^2}\) 

You can observe that as we change the length and breadth, the area of the rectangle changes. We can find the area of a rectangle using the following illustration.


Area of a Rectangle Formula

In the above example, the area of the rectangle whose length is 4 cm and breadth is 3 cm is \(12\text{ cm}^2\).

We have, \(4 \times 3 = 12\)

The area of a rectangle is obtained by multiplying its length and breadth.

Thus, the formula for the area, \(A\) of a rectangle whose length and breadth are \(l\) and \(b\) respectively is the product \({l \times b}\).

\(A=l \times b\)

 
important notes to remember
Important Notes

If \(l\) and \(b\) are the length and breadth, and \(A\) is the area of a rectangle, we have:

  1. \(A=l \times b\)
  2. \(l= \dfrac{A}{b}\)
  3. \(b= \dfrac{A}{l}\)

 

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Area of Rectangle Solved Examples

The area of a rectangle is obtained by multiplying its length and breadth.

Here are a few examples to find the area of a rectangle.

Example 1

 

 

Find the area of the following rectangle

Area of a rectangle examples: Area of a rectangle with dimensions 35 meters and 20 meters

Solution:

The length of the rectangle is, \(l = 35\) cm.

The breadth of the rectangle is, \(b=20\) cm.

The area of the rectangle \(A\) is:

\[ \begin{aligned} A &= l \times b\\[0.2cm] &= 35 \text{ cm} \times 20 \text{ cm}\\[0.2cm]&=700 \text{ cm}^2 \end{aligned}\]

\(\therefore\)Area of rectangle = \({700\text{ cm}^2}\)
Example 2

 

 

Find the area of the following rectangle.

Area of a rectangle examples: Area of a rectangle with dimensions 1 and half kilometers and 3 and one-fourth kilometers

Solution:

The length of the rectangle is,

\(l = 3 \dfrac{1}{4} \) km.

The breadth of the rectangle is,

\(b=1 \dfrac{1}{2}\) km.

The area of the rectangle \(A\) is:

\[ \begin{aligned} A &= l \times b\\[0.2cm] &= 3 \dfrac{1}{4} \text{ km} \times 1 \dfrac{1}{2} \text{ km}\\[0.2cm]&= \dfrac{13}{4}\times \dfrac{3}{2}\\[0.2cm] &= \dfrac{39}{8}\\[0.2cm]&= 4 \dfrac{7}{8} \text{ km}^2 \end{aligned}\]

\(\therefore\)Area of rectangle = \({4 \dfrac{7}{8}\text{ km}^2}\)
Example 3

 

 

The area of a rectangular garden is 4800 \(\text{m}^2\).

Its length is 60 \(\text{m}\). Find its perimeter.

Solved examples of area of a rectangle: finding the perimeter of a rectangular garden whose area and length are given

Solution:

The area of the given rectangular garden is,

\(A = 4800 \text{ m}^2\)

The length of the garden is,

\(l = 60\) m

Let us assume that its breadth is \(b\) meters.

We know that,

\[b= \dfrac{A}{l}\]

Substituting all the values here,

\[b= \dfrac{4800  \text{ m}^2}{60  \text{ m}} = 80 \text{ m}\]

We know that the perimeter of the garden is the sum of all its sides.

\[\begin{align} \text{Perimeter } &= l +l+b+b \\ &= 60+60+80+80 \\ &=280 \text{ m}\end{align}\]

\(\therefore\) Perimeter of garden \(=280 \text{ m}\)
Example 4

 

 

A rectangular garden is of length 20 feet and breadth 17 feet. It is surrounded by a uniform walkway of breadth 2 feet.

Find the area of the walkway.

Solution:

Length of the rectangular garden = \(20\) feet

Breadth of the rectangular garden = \(17\) feet

Breadth of the walkway = \(2\) feet

Solved examples of area of a rectangle: finding the area of the walk way of a garden

Area of the inside rectangle (garden)

\(20 \times 17=340 \text{ ft}^2\)

Area of the outside rectangle (garden+walkway)

\(24 \times 21 = 504 \text{ ft}^2\)

Thus, the area of the walk way is

Area of outside rectangle - Area of inside rectangle

\[ \begin{aligned}&= 504 \text{ ft}^2 -340 \text{ ft}^2 \\[0.2cm]&= 164 \text{ ft}^2 \end{aligned}\]

\(\therefore\) Area of walkway = \({164 \text{ ft}^2}\)
Example 5

 

 

The dimensions of a rectangle are 15 \(\text{cm}\) and 8 \(\text{cm}\).

If each dimension of the rectangle is doubled, how many times is the area increased?

Solution:

The original rectangle is:

Solved example of area of rectangle: find the number of times the area is increased when the dimensions of a rectangle are doubled.

Area of the original rectangle

\(15 \times 8= 120\text{ cm}^2\)

The new rectangle formed when the dimensions of the given rectangle are doubled is:

Solved example of area of rectangle: find the number of times the area is increased when the dimensions of a rectangle are doubled.

Area of the new rectangle

\(30 \times 16= 480\text{ cm}^2\)

Here, 480 (area of the new rectangle) is 4 times 120 (area of original rectangle)

\(\therefore\) The area increases 4 times
 
Challenge your math skills
Challenging Questions
  1. Find the area of the following figure.

Find the area of a the figure whose length and breadth are given.

 

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Practice Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 
 

Maths Olympiad Sample Papers

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

You can download the FREE grade-wise sample papers from below:

To know more about the Maths Olympiad you can click here


Frequently Asked Questions (FAQs)

1. What does the area of a rectangle mean?

The area of a rectangle is the number of unit squares that can fit into it.

The formula for the area 'A' of a rectangle whose length and breadth are 'l' and 'b' respectively is the product l \(\times\) b

2. What is the formula of the area of a rectangle?

The formula for the area 'A' of a rectangle whose length and breadth are 'l' and 'b' respectively is the product l \(\times\) b

3. Define the area of a rectangle.

The area of a rectangle is the number of unit squares that can fit into it.

  
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