Area of Rectangle

Key Concepts

• Properties of a square
• Properties of a rectangle
• Area of a square
• Area of a Rectangle

7.1 Properties of Square:

1. 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:

1. 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:

1. 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