What is the Area of a Square? Clear Your All Doubt!

Area of a Square

Hello readers! Today we will learn about how to calculate the area of a square. Don’t take too much pressure about it. It’s a very easy and simple matter. So, let’s learn.

To calculate the area of ​​a square, first, we need to know what the square is. 

What is a square?

In geometry, a square is a plane structure which has four sides which are equal in length and four equal angles (The value of each angle is 90 degrees). 

Examples of squares

There are many examples of squares here and there around us.

Example no. 1 – Surface of Ludo’s dice

If you have ever played ludo, you must see the dice of it. Every plane surface of Ludo’s dice has four sides and every side is equal in length. So, we can say that every plane surface of Ludo’s dice is a square. 

Example no. 2 – Chessboard

As an example of a square, a chessboard is a great choice. On the one hand, the outside boundary of a chess board is square-shaped, on the other hand, it has 64 small square boxes on the inside. 

Example no. 3 – Floor tiles

Most floor tiles used for construction or decoration are square-shaped. If the floor of your house is covered with tiles, then you will see that there are four sides of the tiles. And if you measure them with a scale, the result you will get is that every side of the tiles is equal in length. The four angles of the tiles will also be 90 degrees if you measure them using any protractor. So, floor tiles are a very good example of a square used in our daily life. 

Example no. 4 – Chocolate

Are you a chocolate lover like me? If yes, then you eat lots of chocolate, right? But while eating chocolate, have you ever noticed the front face of a chocolate cube? The small cubes of a chocolate bar are shaped like squares. So, chocolate cubes are another example of a square. 

What are the Properties of a square?

Following are the main features of a square – 

  • The square has four sides and the length of the four sides is equal.
  • The arms that are opposite to each other are also parallel to each other. 
  • The four angles of a square are equal and each is a right angle (i.e every angle has a value of 90 degrees) 
  • At an angle of 90 degrees, the diagonals of a square bisect each other. 
  • The diagonals of a square are equal in length. 
What’s the Diagonal of Square? 
The diagonal of a square is a straight line that connects the two opposite vertices of the square. 
The diagonal of a square is measured in m, cm, ft, inches etc. 
The formula of Diagonal of square
Suppose the length of every side of the square is – S
Then, the diagonal of the square (D) = S√2
  • Each diagonal of the square divides the square into two congruent triangles.
  • It’s a special parallelogram. 

What is an area?

In simple words, the area of ​​a shape or object is the amount of space that a plane or object occupies. 

Area of a Square

The area of ​​a square means how much space is bounded by the square. Or you can say the area of a square is the amount of space occupied by the square. The area belongs to two-dimensional geometry. 

What is the area of a square? 

The area of a square is equal to the product of the length of the two sides of the square. As the area of a square is equal to the product of any two sides of the square, the area of the square is measured in square units. 

How to calculate the area of a square?

To know the area of a square, at first, we have to only know or measure the length of a side of the square.

Let’s assume that one side of a square is – ‘S’ i.e every side of the square is ‘S’

[Note: As I have told you before that every side of a square is equal in length, so, every side will be – (S)]

In the next step, multiply two sides of the square

It Implies that = S×S = S^2

And now we have got the answer. 

So, the area of a square = S^2 sq. unit

What is the formula for the area of a square?

Now, we have already understood the area of a square.

The area of a square = The product of two sides of the square

Area of a square = (Side×Side) square unit = Side^2 square unit

For example, 

See the image of the square below. 

The length of a side of the square is 4 m i.e the length of every side of the square is 4 m.

So, the area of the square = side×side

= 4m × 4m

= 16 sq. m (square meter) 

What is the Perimeter of a square?

The sum of the four sides of a square is called the perimeter of the square. Mainly the perimeter of a square is the total length of its boundary. Perimeter is measured in terms of m, cm, ft, inches etc. 

What is the formula for the perimeter of a square?

First, look at the square below. 

Let’s assume the lengths of the four sides of this square are – S1, S2, S3 and S4. 

We know every side of a square is equal in length. 

It implies that, S1 = S2 = S3 = S4 = S ( Side of the square) 

Then the perimeter of the square (P) = S + S + S + S =  4 × S

So,

The formula of a square = Side + Side + Side + Side = 4 × Side

For example, 

If the side of a square is 9 m, then what will be its perimeter? 

Ans. 

Length of the side = 9 m

Perimeter of the square = 4 × Side = 4 × 9 = 36 

How to Find the Area of a square? Mathematical examples


Example 1:

Every four sides of a square have a length of 200 cm. Now calculate the area of the square. 

Solution:

As per question,

the side of the square = 200 cm = 2 m

Area of the square = side × side

= 2 m × 2 m

= 4 sq. m.


Example 2:

The diagonal of a square is 300 cm. What is the length of every side of the square? 

Solution:

As per the question, 

the diagonal of the square = 300 cm = 3 m

Let’s assume the length of every side of the square = S

We know that in the case of a square, 

Diagonal = Side √2

Or, 3 = S √2 (S = Side) 

Or, S = (3 ÷ √2) m

Or, S = 2.121 m

So, the length of every side of the square is 2.121 m. 


Example 3:

If the length of the diagonal of a square is 6 m, then what is its area? 

Solution:

As per the question,

the diagonal of the square = 6 m

Let’s assume the length of every side of the square = S

We know that in the case of a square, 

Diagonal = Side √2

Or, 6 = S√2 (S = Side) 

Or, S = (6÷√2) m

Or, S = 4.242 m

Now, the area of the square = S× S (Side × Side) 

= 4.242 m × 4.242 m

= 17.994 sq. m.


Example 4:

The perimeter of a square wall is 60 m. Then find the length of the wall. 

Solution:

As per the question, 

the perimeter of the square wall = 60 m

We know that in the case of a square, 

Perimeter (P) = 4 × S (Side) 

Or, 60 = 4 × S

Or, S = (60 ÷ 4) m

Or, S = 15 m

So, the length of the wall is 15 m. 


Example 5:

If the area of a square floor is 900 sq. m, then what is its side length? 

Solution: 

As per the question, 

The area of the square floor is 900 sq. m. 

We know that, the area of a square = S × S (S = Side) 

Or, 900 = S^2

Or, S = √900 m

Or, S = 30 m

So, the length of every side of the floor is 30 m.


Example 6:

If the area of a square is 400 sq. m, then what is its perimeter? 

Solution:

As per the question, 

The area of the square = 400 sq. m

We know that the area of a square = S × S (S = Side) 

Or, 400 = S^2

Or, S = √400 m

Or, S = 20 m

Now, perimeter (P) = 4 × S

Or, P = (4 × 20) m

Or, P = 80 m

So, the perimeter of the square is 80 m. 


Example 7:

A square room has a total floor area of 2700 sq. m. The side of each square tile is 300 cm. How many tiles are required to cover the entire floor. 

Solution:

As per question, 

The area of the square floor = 2700 sq. m. 

The side of each square shaped tile = 300 cm = 3 m

Area of one tile = S × S (S = Side) 

= 3 m × 3 m

= 9 m

The required number of tiles = Area of the floor ÷ Area of one tile

= 2700 ÷ 9

= 300 

So, 300 tiles are required to cover the floor. 


Example 8:

A square wall of 30 m in length is to be painted. If the cost of painting per sq. m is ₹5, find out the cost of painting the whole wall. 

Solution:

As per the question, 

The length of the wall = 30 m. 

Now, the area of the wall = 30 m × 30 m  = 900 sq. m

Cost of painting per sq. m = ₹5.

So, the cost of painting 900 sq. m = ₹(900 × 5) 

= ₹4500

So, the cost of painting the whole wall is ₹4500.


Example 9:

The diagonal of a square is 7√2 m. Find out its perimeter. 

Solution:

As per the question, the diagonal of the square = 7√2 m. 

We, know that diagonal of a square = S√2 (S = Side) 

Or, 7√2 = S√2

Or, S = 7 m

So, the perimeter of the square = 4 × S = 4 × 7 = 28 m. 


Example 10:

What is the length of a square garden which area is 1600 sq. m? 

Solution: 

As per the question, 

The area of the square garden = 1600 sq. m

As we know, 

Area of a square = S × S (S = Side) 

Or, 1600 = S^2

Or, S = √1600 m

Or, S = 40 m

So, the length of the garden is 40 m. 


FAQs

What is the area of a 4 cm square? 

The length of the square = 4 cm 

So, the area of a 4 cm square = s × s = 4 cm × 4 cm = 16 cm2

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