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Area of Rectangle

Last Updated : 18 Feb, 2024
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A rectangle is a quadrilateral in which opposite sides are equal and parallel. Area of Rectangle is the region covered inside the boundaries of the rectangle.

In this article, we are going to study about area of rectangle in detail, including its formula and examples.

What is Area of Rectangle?

The area of a rectangle is the space enclosed by the boundaries of the rectangle. We can also say that the space enclosed by the perimeter of the rectangle is the area of a rectangle.

Area of Rectangle

Area of Rectangle

Unit of Area of Rectangle

The area of a rectangle is measured in square units and the standard unit for measuring the area of a rectangle is m2. Other units widely used for measuring the area of the rectangle are cm2, mm2, and others.

Side

Area

meter(m)  m2   or (meter)2       
centimeter(cm) cm2  or (centimeter)2

Area of Rectangle Formula

Area of rectangle is the multiplication of length (L) and breadth (B).

Area of rectangle Formula, A = L x B

where ,
L is the length of the rectangle
B is the breadth of the rectangle

Note:- If the unit of length and breadth is not exact then it should be transformed into one unit. For e.g. If the length is in cm and breadth in m then both dimensions should be adjusted either to m or cm.

How to Find Area of Rectangle?

The area of the rectangle is defined as the product of its length and breadth. Following are the steps that help calculate the area of the rectangle,

Step 1: Note down the dimensions of the rectangle.

Step 2: Calculate the product of the length and breadth of the rectangle.

Step 3: Write the answer in respective square units.

Example: Find the area of a rectangle whose length is 20 inches and breadth is 50 inches.

Solution:

The formula for area of rectangle is given:

Area = L × B

Area = 20 × 50

Area = 1000 inches2

Thus, the required area is 1000 inches2

Area of Rectangle using Diagonal

The area of the rectangle can be found by two methods which are:

Method 1

We can find the value of the missing side using the Pythagoras theorem and then find the area. Let us understand this using an example.

The diagonal of the rectangle is the line joining opposite vertices. The diagonal of the rectangle is calculated using Pythagoras’s Theorem

Area of Rectangle using Diagonal

Method 1 to find the Area of the Rectangle

(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

Area = √(Diagonals2 – Breadth2) × Breadth

Area = Breadth √(Diagonals2 – Breadth2)

Method 2

If both the diagonals of the rectangle are given then its area can be found with the help of the area of the quadrilateral formula.

Let a rectangle ABCD have diagonals as AC and BD and their length is d1 and d2 then its area is given by,

Area of rectangle ABCD = 1/2 × d1 × d2

Example: Find the area of a rectangle whose length of the diagonals is 10 cm and 14 cm.

Solution:

The formula for area of rectangle is,

Area = 1/2 × d1 × d2

Area = 1/2 × 10 × 14

Area = 70 cm2

Thus, the area of required rectangle is 70 cm2.

Area of Rectangle using Perimeter

To calculate the area of a rectangle using the perimeter and one dimension follow the following steps,

Step 1: Note the perimeter and the given dimension.

Step 2: Use the perimeter formula to find the other dimension.

Step 3: Use the area of the rectangle formula and substitute the required value obtained in Step 2

Step 4: Simplify the expression and add unit to get the final answer.

The example given below explains the above concept.

Example: Find the area of a rectangle when the perimeter is 28 cm and the breadth is 8 cm.

Solution: 

Given,

Perimeter of Rectangle = 28 cm

length = 8 cm

breadth(b) = ?

Using Perimeter of rectangle formula,

Perimeter of rectangle = 2 (l + b)

28 = 2 (8 + b)

14 = 8 + b

b = 6 cm

Thus the breadth of rectangle is 6 cm

Area of Rectangle = l × b

= 8 × 6 = 48 cm2

Thus, the area of the Rectangle is 48 cm2

Area of Rectangle Formula Derivation

Area of rectangle is the product of length and breadth. This can be derived by dividing the rectangle into two triangles. The triangles are equal as the base and height of the two triangles will be equal. 

Let’s derive the formula for the area of rectangle, the image given below shows that a rectangle is made by joining two equal right-angle triangles.

Area of a Rectangle Formula Derivation

Area of a Rectangle Formula Derivation

  • Area of Rectangle = 2 (Area of Triangle)
  • Area of Rectangle = 2 (1/2 × Base × Height)
  • Area of Rectangle = 2 (1/2 × AB × BC)
  • Area of Rectangle = AB × BC
  • Area of Rectangle = Length × Breadth.

Thus, the area of rectangle formula is derived.

Related :

Solved Examples on Area of Rectangle

Example 1: The length and width of a rectangle are 6 units and 3 units, respectively. Find the area of rectangle.

Solution:

Given,  

length = 6 unit
breadth = 3 units

Area of rectangle =  length × breath
                            =  6 × 3
                            = 18 square units

Thus, the area of given rectangle is 18 square units

Example 2: The height of a rectangular net is seen to be 20 cm. Its area is seen to be 260 cm2. Find the width of the provided net.

Solution: 

Given, 

Height = 20 cm
Area = 260 cm2

Area of Rectangle = width × height

Therefore, 

width = Area / height

width = 260/20

width = 13 cm

Thus, the width of the rectangle is 13 cm

Example 3: The height and width of a rectangular desk are 40 m and 20 m, respectively. If a carpenter charges ₹ 2 per m2 for his work, how much would it cost to make the whole desk?

Solution:

Given, 

Height of Desk = 40 m
Width of Desk = 20 m

Area of top of Desk = width of desk × height of desk

Area of top of Desk = 40 × 20

Area of top of Desk = 800 m2

At the cost of ₹ 2 per m2

The cost for making top of the desk is 800 × 2 = ₹ 1600

Example 4: A wall whose length and width are 60 m and 40 m respectively needs to be painted. Find the quantity of the paint required if 1 litre of paint can paint 400 m2 of the wall.

Solution:

Given, 

Length of wall = 60 m

Width of wall = 40 m

Area of wall = width × length

Area of wall = 60 × 40

Area of wall = 2400 m2

Paint required for 400 m2 of wall = 1 litre   (given)

Paint required for 2400 m2 of wall = 2400 / 400 × 1 = 6 litre.

Thus, the paint required to paint the wall is 6 litre.

Practice Questions on Area of Rectangle

Q1: What is the area of a Rectangular Field of length 15 m and width 8 m.

Q2: Find the Area of a Rectangle whose length is twice its breadth and perimeter is 72 cm.

Q3: What is the cost of tiling a floor of length 10 m and with 11 m at the rate of 15 rupees per square metre?

Q4: How many boxes of dimension 10 cm by 9 cm can be placed on a floor of 10m by 9 m.

FAQs on Area of Rectangle

What is Area of Rectangle Formula?

Area (A) of rectangle formula is the product of the length and breadth. It can be defined as the space occupied by its boundaries.

What is the Unit of Area of Rectangle?

The unit of the area of rectangle are meter2, centimeter2, inches2, etc. In general, it is unit2.

What is the Perimeter of Rectangle Formula?

The perimeter of rectangle is the sum of the length of all its boundaries. The formula for perimeter of rectangle is given as;

P = 2 (Length + Breadth)

How To Find the Area of Rectangle?

For a rectangle whose length is l and breadth is b then its area can be calculated by using the formula,

Area = l × b

How to find the Area of Rectangle with a Diagonal?

The area of the rectangle when its diagonal is given is calculated using the formula,

Area = 1/2 × d1 × d2

where
d1 is the first diagonal.
d2 is the second diagonal.

How to find the Area of Rectangle when Perimeter is given?

The area of a rectangle when its perimeter and any one side is given can be calculated by,

Step 1: Use the perimeter of the rectangle formula to find the relation between length (l) and breadth (b).

Step 2: One dimension is already given. Use the relation to find the other dimension.

Step 3: When both dimensions are known use the area formula to find the area.

How to calculate the Area of Quadrilateral with 4 different sides?

The area of a quadrilateral with all fours sides different and both diagonal given are, 

Area = 1/2 × d1 × d2

where
d1 is the first diagonal.
d2 is the second diagonal.

Is Area of Rectangle equal to Area of Square?

No, it is not necessary that the area of the rectangle is equal to the area of square. The condition where both the areas are equal is when the length and breadth in a rectangle are equal.



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