Table of Contents
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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.
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".
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.
Let us draw unit squares inside the rectangle.
Each unit square is a square of length 1 cm.
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 \({l \times b}\).
| \(A=l \times b\) |
If \(l\) and \(b\) are the length and breadth, and \(A\) is the area of a rectangle, we have:
- \(A=l \times b\)
- \(l= \dfrac{A}{b}\)
- \(b= \dfrac{A}{l}\)
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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
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.
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.
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
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:
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:
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 |
- Find the area of the following figure.
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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:
- IMO Sample Paper Class 1
- IMO Sample Paper Class 2
- IMO Sample Paper Class 3
- IMO Sample Paper Class 4
- IMO Sample Paper Class 5
- IMO Sample Paper Class 6
- IMO Sample Paper Class 7
- IMO Sample Paper Class 8
- IMO Sample Paper Class 9
- IMO Sample Paper Class 10
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.