1. Area of a Rectangle
A rectangle is a quadrilateral with four right angles. It has two equal lengths and two equal breadths. The area of a rectangle tells us how much surface it covers—it measures the amount of space inside the rectangle.
To find the area, we look at how many square units fit inside the shape. These square units can be cm², m², or any other unit of area depending on the given values.
1.1. Definition of Area
The area of a rectangle is defined as the product of its length and breadth. This means we multiply the measure of one side by the measure of the adjacent side to find how much space is enclosed.
2. Area Formula
If the rectangle has:
- length = \(l\)
- breadth = \(b\)
then its area is given by the formula:
\( A = l \times b \)
2.1. Why the Formula Works
Imagine filling the rectangle with small 1 × 1 squares. Along the length, you can fit \(l\) squares. Along the breadth, you can fit \(b\) squares.
So in total, the number of 1 × 1 squares that fit inside the rectangle is:
\( \text{Total squares} = l \times b \)
This multiplication gives the area of the rectangle.
3. Examples
Let’s see how to apply the area formula in simple problems.
3.1. Example 1
A rectangle has length \(l = 10\,\text{cm}\) and breadth \(b = 4\,\text{cm}\). Its area is:
\( A = l \times b = 10 \times 4 = 40\,\text{cm}^2 \)
3.2. Example 2
A rectangular plot has length \(l = 25\,\text{m}\) and breadth \(b = 18\,\text{m}\). The area covered is:
\( A = 25 \times 18 = 450\,\text{m}^2 \)