# Area of Rectangle : Concept & Formula

## What is Rectangle?

Rectangle is a Quadrilateral in which two opposite sides are equal and parallel

Key Features of Rectangle
(a) Opposite sides equal and parallel
(b) All angle measure 90 degree

## What is Area of Rectangle?

Area of Rectangle is the amount of space covered within the boundary of the figure

Given above is the rectangle ABCD

The surface covered inside the rectangle (marked in red color) is the Area of Rectangle

Explanation 02

Area of rectangle can also be understood as the number of square units present inside the rectangle

Given above is the rectangle ABCD

Note that the rectangle is made of 8 squares.

The area of each square is 1 sq. cm

We can say that area of rectangle ABCD is 8 square unit.

## Area of Rectangle Formula

The Area of Rectangle is given by following formula:

Length = Longer side of Rectangle

Example 01
Find the area of below rectangle

Method 01
Using Formula

We know that;
Area of Rectangle = Length x Breadth

Length = 5 cm

Putting Values in the formula, we get

Area of Rectangle = 5 x 2 = 10 sq cm

Method 2
Finding the number of squares

You can observe that the rectangle ABCD is made of 10 squares of 1 cm each

Area of Square = 1 x 1 = 1 sq. cm

Area of Rectangle
⟹Number of Square x Square Area
⟹ 10 x 1
⟹ 10 sq cm

Hence area of rectangle is 10 sq. cm

Example 02
Find the area of below rectangle

Method 01
Using Formula

Area of Rectangle
⟹ 6 x 4
⟹ 24 sq. cm

Method 02
Number of unit squares

There are 24 squares in the above rectangle

Area of 1 square = 1 sq unit

Area of Rectangle = Area of square x Number of Square

Area of Rectangle = 1 x 24 = 24 sq cm

## Proof of Area of Rectangle formula

Given
ABCD is a rectangle with diagonal BD
The diagonal BD divides the rectangle into two triangles ABD & DCB

AB = DC = Length

To Prove
Area of Rectangle = Length x Breadth

Solution

Take triangle ABD

Area of triangle = (1/2) x Base x Height

Area of Triangle ABD = (1/2) x AB x AD

Take Triangle DBC

Area of triangle DBC = (1/2) x DC x BC

We know that:
Area of Rectangle ABCD

⟹ Area of triangle ABD + DBC

⟹ (1/2) [AB . AD + DC . BC]

⟹ (1/2) [ 2 Length . Breadth]

Hence Proved

## Area of Rectangle Solved Problems

(01) In a rectangle if length is 10 cm and breadth is 5 cm. Find the area of rectangle

Given
Length = 10 cm

We know that;
Area of Rectangle = Length x Breadth

Putting the values

Area of Rectangle = 10 x 5 = 50 sq cm

Hence, 50 sq. cm is the area

(02) Find the area of below rectangle

Given
Length = 8 cm

Area of rectangle = Length x Breadth

Putting the values

Area of rectangle = 8 x 3 = 24 sq. cm

Hence, 24 sq cm is the required solution

(03) Find the area of below rectangle

Solution

There are total 8 squares inside the rectangle

Area of a square = 1 sq. meter

Area of rectangle
⟹ Area of Square x Total square

⟹ 1 x 8

⟹ 8 sq. meter

Hence, 8 sq. meter is the solution

(04) Find the area of rectangle whose length is 7 cm and breadth is 3 cm

Given
Length of rectangle = 7 cm
Breadth of rectangle = 3 cm

Area of rectangle = Length x Breadth

Putting the values

Area of rectangle = 7 x 3 = 21 sq cm

Hence, 21 sq cm is the solution

(05) Find the area of below rectangle

Given
Length of rectangle = 3 cm
Breadth of rectangle = 9 cm

Area of Rectangle

⟹ 3 x 9

⟹ 27 sq. cm

(06) Find the area of below rectangle

Solution

Total number of squares inside rectangle = 12

Area of square = 1 sq m

Area of rectangle
⟹ Area of Square x Number of Square

⟹ 1 x 12

⟹ 12 sq meter

Hence area of rectangle is 1 sq meter

(07) The area of rectangle is 3200 sq. cm. If the length of rectangle is 80 cm, then find the breadth

Given
Area of rectangle = 3200 sq cm

Length = 80 cm

Area of rectangle = Length x Breadth