Area of Rectangle Formula: What is area? What is a rectangle? What is the area of a rectangle and how does one calculate the area of a rectangle? In this article, we have explained all concepts related to the area of a rectangle suitable for grades 5, 6 and 7 of CBSE, ICSE, UP Board, RBSE and other state boards.
Area: Area is the amount of space inside a two-dimensional shape, usually measured in square units.
Rectangle: A rectangle is a simple four-sided shape with two pairs of parallel sides. It's a fundamental shape with numerous applications in both mathematics and daily activities. A rectangle is defined by its length (L) and width (W)/ Breadth (B), both of which have distinct values.
Definition: What is the Area of a Rectangle?
The area of a rectangle is the space enclosed between its outer edges. It is equal to the product of its length and breadth.
Area of a Rectangle Formula
Multiply the length (l) of the rectangle with the breadth / width (b) to get its area.
Area of rectangle = length (l) X breadth (b) square units
What is the length of a rectangle?
The longer side of the rectangle is called its Length.
What is the width of a rectangle?
The shorter side of the rectangle is called its Width
Unit of Area of Rectangle
The unit of any rectangle’s area is square units.
For example, centimetre square / cm2 or metre square / m2.
How to Find the Area of a Rectangle?
Steps to Find the Area of a Rectangle are listed below:
Step 1: Identify length and breath of the rectangle.
Step 2: Multiply length and width to get the area of the rectangle.
Step 3: Use square units to finish the answer.
How to Find the Length of a Rectangle using Breadth?
To find the length of rectangle whose width is given, use this formula:
Length = Area of a rectangle/ width
i.e L = A/ b
How to Find the Width of a Rectangle using Length?
To find the width of rectangle whose length is given, use this formula:
Width = Area of a rectangle/ length
i.e B = A/ l
How to Find the Area of a Rectangle using Diagonal?
If you need to find the area of a rectangle using a diagonal, you would have to calculate the length or breadth of the rectangle using the diagonal. Use Pythagoras theorem to find the missing length or breadth value since the vertices are at 90 degree angle.
(Diagonal)2 = (Length)2 + (Breadth)2
Length2 = (Diagonals2 – Breadth2)
Length = √(Diagonals2 – Breadth2)
The formula for the area of a rectangle is calculated by:
Area = Length × Breadth
OR
Area = √(Diagonals2 – Breadth2) × Breadth
Area = Breadth √(Diagonals2 – Breadth2)
How to Find the Area of a Rectangle using Perimeter?
If the perimeter and one side of a rectangle are given, then you must find out the missing side of the rectangle by using the Perimeter of Rectangle formula.
Perimeter of a rectangle = 2 (l + b)
Let us assume that the breadth of the rectangle is missing, then
b = (perimeter - 2l)/ 2
The formula for the area of a rectangle is calculated by:
Area = l X b
Area of Rectangle Solved Examples
Que 1: Calculate the area of a rectangle with a width of 5 cm and a length of 20 cm.
Solution:
Length (l) = 20 cm
Breadth (b) = 5 cm
Area Hence, area = l x b = (5 x 20) sq cm = 100 sq cm
Que 2: A rectangular table-cloth has a length of 12 feet and area of 168 sq feet. What is the breadth of the carpet?
Solution:
Length (l) = 12 feet
Area (A) = 168 sq ft
Breadth = A/l = 168 sq ft / 12 ft = 14 ft
Que 3: The length of a rectangular carpet is twice its breadth. If the breadth of the carpet is 4 m, find the area of the carpet.
Solution:
Breadth (b) = 4m
Acc to the question, l = 2b = 8m
Therefore, area of the carpet = l x b = 8m x 4m = 32 sq m