Area of a Rectangle – Formula, Examples & Practice
Key Concepts
- Properties of a square
- Properties of a rectangle
- Area of a square
- Area of a Rectangle
7.1 Properties of Square:
- What is a Square?
A SQUARE has
- Four sides.
- Four corners.
Note: All sides are of equal length in a square.
Example of Square:
7.2 Properties of Rectangle:
- What is a Rectangle?
A RECTANGLE has
- Four sides.
- Four corners.
Note: The opposite sides are of equal length in a rectangle.
Example of Rectangle
How to Measure Area of a Square
The Area of a Square by multiplying the length of the two sides. Since the length of the sides are the same in a Square as given in below picture.
If Side = “S”
THE AREA OF A SQUARE = S x S
Area is measured in “square” units
Note: S x S is not equal to 2 x S.
Number of Squares = 16
Area of a Square = 16 square units
Area of a Square = Side x Side
= 4 x 4
= 16 Square units
Assessment: Try this
- Calculate the area of the square floor area whose length of each side is 10 Mts?
Note:
- All the sides in a square have the same length.
- All the lengths are measured in units.
- Total area should me represented in square units only.
Solution:
Length of a each side = 10 Mts
Side = 10 Mts
Area of a Square = Side x Side
= 10 Mts x 10 Mts
Total floor area = 100 Sq.Mts
Note: Sq.Mts represents Square Meters
How to Measure Area of a Rectangle:
The Area of a Rectangle is found by multiplying the length and the width of a rectangle.
As the opposite sides are the same in a rectangle Area is calculated as
Area of the Rectangle = Length * Width
Note: Both length and width of opposite side are equal.
Number of Squares = 12
Area of rectangle = 12 square units
Finding Area using Array Method
Total number of Squares = Rows x columns
= 3 x 4
= 12
Total Area of a Rectangle = Total number of squares = 12 square units
Number of Squares = 15
Area of rectangle = 15 square units
Finding area using Array Method
Total number of Squares = Rows x columns
= 4 x 6
Area of a Rectangle = Total number of squares = 24 Square units
Example: Lets apply
- Calculate the area of the road whose length is 10 mts and width is 8 Mts?
Note:
- Opposite sides of a rectangle are equal.
- All the lengths and width of a area should be calculated on same units.
- Total area should me represented in square units only.
Solution:
Length of a each side = 10 Mts
Width of a each side = 8 Mts
Length = 10 Mts
Width = 8 Mts
Area of a Rectangle = Length x Width
= 10 Mts x 8 Mts
Total Road area = 80 Sq.Mts
Note: Sq. Mts represents Square Meters
Every square is a rectangle
For Example side of a square = 6 feet
Area of the square = Side x side = 6 x 6 = 36 square feet
Foe a square length = width = side
Area = length x width = 6 x 6 = 36 square feet
Every Rectangle is not a Square
For Example if Length = 6 feet width = 4feet
Area = length x width= 6 x 4 = 24 square feet
For a rectangle length ≠ width
Both sides of the rectangle are not equal so Rectangle cannot be a square
Assessment
Jack is painting a wall in the school. The length of the wall is 6 feet and the width of the wall is 8 feet. The paint can Jack brought covers 40 square feet. Does Jack need more paint to paint the wall completely ? Discuss
Area of the wall in Mike’s room is 63 Sq feet. The length of the wall is 7 feet high. How much is the width of the wall?
Exercise:
- Jack is painting a wall in the school. The length of the wall is 6 feet and the width of the wall is 8 feet. The paint can Jack brought covers 40 square feet. Does Jack need more paint to paint the wall completely ? Discuss
2. Area of the wall in Mike’s room is 63 Sq feet. The length of the wall is 7 feet high. How much is the width of the wall?
What we have learnt:
- In a Square all sides are of equal length
- In a Rectangle opposite sides are of equal length
- Area is measured in “square” units
- Area of the Square = S x S
- Area of the Rectangle = Length * Width
- Area is measured using Standard units
- Every Square is a Rectangle
- Every Rectangle is not a Square
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