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:
Area = Length x Breadth
Length = Longer side of Rectangle
Breadth = Shorter side
Example 01
Find the area of below rectangle
Method 01
Using Formula
We know that;
Area of Rectangle = Length x Breadth
Length = 5 cm
Breadth = 2 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
⟹ Length x Breadth
⟹ 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
AD = BC = Breadth
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) [Length . Breadth+ Length . Breadth]
⟹ (1/2) [ 2 Length . Breadth]
⟹ 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
Breadth = 5 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
Breadth = 3 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
⟹ Length x Breadth
⟹ 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
3200 = 80 x Breadth
Breadth = 3200/80 = 40 cm
Hence, breadth is 40 cm