 # Area of Rectangle

Area of rectangle is the region covered by the rectangle in a two-dimensional plane. The surface area of a 2D shape, rectangle is calculated by its formula which includes its length and breadth. A rectangle is a four-sided polygon having the length of the opposite sides to be equal. Since each angle of measure 90 degrees, it can also be termed as an equiangular quadrilateral.  In this article, we will discuss the rectangle definition, area of rectangle formula, and also surface area of a rectangle like lateral surface area and total surface area in detail.

## Rectangle Definition

A rectangle can also be defined as a parallelogram containing opposite sides equal and parallel in it. A rectangle is called a square if all its sides are of equal length. ## Area of Rectangle Formula

The size of any object can be measured in many different ways. For instance, we all normally calculate how tall the building or the size of a swimming pool how deep it is.

Well, what is the area of a rectangular object, how to find out the area of the rectangle?

The area of a rectangle is calculated in units by multiplying the width (or breadth) by the Length (or Height) of a rectangle. The mathematical formula for calculating the total and lateral surface area of a rectangle is mentioned below:

The formula for the Area of a Rectangle
Lateral Surface Area A = 2(l + b)
Total Surface Area A = l × b

The area of any rectangle is calculated once its length and width are known. By multiplying length and breadth, the rectangle’s area which will be in square-units dimension. In the case of a square, the area will become length2. The main difference between square and rectangle is that the length and width are equal.

## How to Calculate the Area of a Rectangle

Follow the steps below to find the area:

Step 1:  Note down the dimensions of length and width from the given data.

Step 2: Multiply length and width values

Step 3: Write the answer in square units.

Below are some special formula related to the rectangle area.

1. How to find the area with diagonal of rectangle and width

Formula: Area = $Width\ \sqrt{(Diagonal^2 – Width^2)}$

1. Find a missing side length when the area is known

Formula: Length = Area/Width

### Area of Rectangle Example

Example 1: Find the area of the rectangle whose length is 15 cm and the width is 4 cm?

Solution:

Given,

Length = 15 cm

Width = 4 cm

Area of a rectangle = Length × Width

15 × 4  = 60

So the area of rectangle = 60 cm2

Example 2: Find the area of a rectangular blackboard whose length and breadth are 120 cm and 100 cm respectively.

Solution:

Length of the blackboard = 120 cm = 1.2 m

Breadth of the blackboard = 100 cm = 1 m

Area of the blackboard = area of a rectangle = length x breadth = 1.2 m x 1 m = 1.2 square-metres

Example 3: The length of a rectangular screen is 15 cm. Its area is 180 sq. cm. Find its width.

Solution:

Area of the screen = 180 sq. cm.

Length of the screen = 15 cm

Area of a rectangle = length x width

So, width = area/length

Thus, width of the screen = 180/15 = 12 cm

Example 4: The length and breadth of a rectangular wall is 75 m and 32 m. Find the cost of painting the wall if the rate of painting is Rs 3 per sq. m?

Solution:

Length of the wall = 75 m

The breadth of the wall = 32 m

Area of the wall = length x breadth = 75 m x 32 m = 2400 sq. m

For 1 sq. m of painting costs Rs 3

Thus, for 2400 sq. m, the cost of painting the wall will be = 3 x 2400 = Rs 7200

Example 5: A floor whose length and width is 50 m and 40 m respectively needs to be covered by rectangular tiles. The dimension of each of the tile is 1 m x 2 m. Find the total number of tiles that would be required to fully cover the floor.

Solution:

Length of the floor = 50 m

The breadth of the floor = 40 m

Area of the floor = length x breadth = 50 m x 40 m = 2000 sq. m

Length of one tile = 2 m

The breadth of one tile = 1 m

Area of one tile = length x breadth = 2 m x 1 m = 2 sq. m

No. of tiles required = area of floor/area of a tile = 2000/2 = 1000 tiles