Area of Rectangle

There are various rectangular shapes that we see in our daily lives, such as computer screens, cell phones, tables and books.
Have you ever thought about how much area is occupied by your book which is placed on the table? So, in this article, we will dive into the definition of the rectangle, its properties and the formula for calculating its area in depth.

What is a Rectangle?

A rectangle is a closed two-dimensional (2-D) shape. It is a four-sided polygon, with all the internal angles equal to 90 degrees.

In the above figure, AB is the length, whereas BC is the breadth of the rectangle ABCD. We use length and breadth to find the area and perimeter of the rectangle.

Properties of Rectangle

→ It is a flat and closed shape having 4 sides, 4 angles and 4 vertices. It is a quadrilateral.
→ It has 2 dimensions, namely, length and width.
→ Every angle of a rectangle measures 90^o.
→ The opposite sides of a rectangle are equal and parallel to each other.
→ It has 2 diagonals of equal length.
→ The sum of all of its interior angles is 360^o.

Area of Rectangle

Area is defined as the amount of space occupied by a two-dimensional figure. There is a formula The formula for the area of a rectangle is:

Area of the Rectangle Using Diagonal

We can determine a rectangle's area even if we only know its diagonal and one side (length or breadth). The diagonal of a rectangle is represented in the given figure.

Where,
d: Diagonal of the rectangle
l: Length of the rectangle
b: Breadth of the rectangle

The formula for the diagonal of a rectangle is derived from Pythagoras' theorem. The formula of the diagonal is:

We know that
Area of the rectangle = Length x Breadth
Now substituting the value of length in the formula of the area of the rectangle, we will get

Similarly, if the diagonal and length of the rectangle are given, then its area can be calculated using the given formula:

Units of Area of Rectangle

The unit of area for a rectangle or any two-dimensional shape can be measured in square metres (m²), square centimetres (cm²), square inches (in²), square feet (ft²) and square yards (yd²) based on the system of measurement being used.

Click Here to Read About: Formula for Perimeter of a Rectangle

Golden Rectangle

There is a special rectangle called the Golden rectangle. A golden rectangle is a rectangle whose 'length to width' ratio is similar to the golden ratio, 1: (1+?5)/2 which is:

Hence, the ratio between the sides of this rectangle is 1: 1.618. For instance, if the width is about 1 foot long, then the length will be 1.168 feet long.

Solved Examples of Areas of a Rectangle

1. What is the area of a rectangle whose length and breadth are 10 cm and 8 cm, respectively?

Solution:
Given:
Length = 10 cm
Breadth = 8 cm
Area of a rectangle = length x breadth
= 10 x 8
= 80 square centimetres or cm²
Hence, the area of the rectangle is 80 square centimetres (cm²).

2. If the area of a rectangle is 120 m² and the breadth is 5 m, then calculate the length of the rectangle in cm.

Solution:
Given:
Area = 120 m²
Breadth = 5 m
If we rearrange this formula, the Area of a rectangle = length x breadth
We get the formula for length, which is given below:

Length = $\frac{\frac{\mathrm{Area}}{}}{\frac{\mathrm{Breadth}}{}}$
= $\frac{\frac{\mathrm{120}}{}}{\frac{\mathrm{50}}{}}$
= 24 m
Hence, the length of the triangle is 24 m.

3. A rectangular field is 50 m long and 30 m wide. What is the area of the field?

Solution:
Given:
Length = 10 cm
Breadth = 8 cm
Area of a rectangle = length x breadth
= 50 x 30
= 1500 m²
Hence, the area of the rectangular field is 1500 square metres (m²).

Frequently Asked Questions

1. Can the area of a rectangle be a negative number?

Answer: No, the area cannot be negative. Length and width are both measured in non-negative units and their product (the area) is always non-negative.

2. What are the units used to measure the area of a rectangle?

Answer: The units for the area are square units, such as square metres (m²), square centimetres (cm²), square feet (ft²), etc., depending on the units used for length and width.

3. What happens to the area if you double the length of the rectangle but keep the width the same?

Answer: If you double the length while keeping the width constant, the area of the rectangle will also double. This is because the area is directly proportional to both length and width.