### 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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