Table of Contents

**What is a Square?**

Square is a plane dimensional figure. It is a form of quadrilateral which has four sides and all sides are of equal length, and each angle is 90`. There are four vertices of a square. And also four edges of the square. Square is also a rectangle. We see a number of squares in our daily routine like the wall clock of the square shop, some of the game boards, a slice of bread, and many others.

**Area of a Square**

The area of the square means the number of units which is required to complete or fill the square. As we discussed above that all sides of a square are equal, then we can find the area of the square by calculating the products of their two sides. The area of the square can be calculated with different dimensions like with the help of a parameter, and with the help of a diagonal. In other words area of square means, the total area that is covered by a closed two-dimensional plane figure which has equal sides and equal angles and each angle is 90 degrees.

**Common unit:**

The common unit which is mostly used while calculating the area of the square is square meter, square cm, square inches, etc.

Area of the square formula:

The very simple and majorly used formula to calculate the area of the square is:

A=side*side It means we can calculate the area of the *square by multiplying the side into the side. The side of the *square is denoted by the word ‘a’. So it can also be written as: *

**A= a*a**

Let us clear this formula with the help of some examples:

**Some Examples:**

**Example 1: **Calculate the area of a square with the sides of 9 centimeters.

**Solution:**

Here in the question, the side of the square is 9cm.

Then, by applying the formula:

A= side-side* and by putting the value of side= 9cm, A=9*9

A=81cm2

**Example 2: **Calculate the area of a square with the side of 6cm.

Here in the question, the side of a square given is 6cm.

Then, by applying the formula:

A= side*side* And by putting the value of side that is 6cm. A=6*6

A=36cm2

Example 3: Calculate the area of the square when a is given 11cm.

**Solution:**

Here, a is given of length 11cm.

And a denotes the side of a square. So, the side of the square is 11cm.

Then, by applying the formula to calculate the area of a square, we get

A= side*side * A= 11**11

A= 121cm2

We can calculate the area of the square by many other dimensions.

**The perimeter of square:**

The perimeter of a square means the sum of all sides of the square. In other words,

the perimeter of a square means the total length of all sides of the square.

It is calculated by the following formula:

P= a+a+a+a

Here, a denotes to the side of the square.

It can also be written as:

P=4a Or P= 4 side

Now, let us take some examples to understand quickly.

**Example 1: **Calculate the perimeter of a square when the side given is 4cm.

**Solution:**

Here, the side of a given square is 4cm.

Then,

By applying the formula:

P=4*side P=4*4

P= 16cm2

And, it is also solve by applying following formula:

P= a+a+a+a

P= 4+4+4+4

P= 16cm2

**Example 2:** Calculate the perimeter of a square when the side given is 9cm.

**Solution:**

Then, the side given in the square is 9cm.

By applying the formula to calculate the perimeter of a square.

P= a+a+a+a

P= 9+9+9+9

P=36cm2

How to calculate the area of a square when the perimeter of a square is giv**en?**

Let us clear this by few examples:

**Example 3: **Calculate the area of the square when the perimeter of a square given is 16cm.

The perimeter given in the question is 16cm.

By applying the formula of the perimeter of a square:

P=4*side 16=4*side

16/4= side

Side = 4cm.

Then, by applying the formula of area of a square:

A= side**side A= 4*4

A= 16cm2

**Example 4: **Calculate the area of a square when the perimeter of a given square is 24cm.

According to the question, the perimeter of a given square is 24cm.

Then, by applying the formula of the perimeter of the square we get:

P= 4side 24= 4side

24/4= side

Side=6cm.

Now, we get the side of a square is 6cm.

After that, we calculate the area of the square by applying the formula of area of

square, we get

A= side**side A= 6*6

A= 36cm2

**Example 5: ** Calculate the area of a square when the perimeter of a square is 30cm.

**Solution:**

Now, as per the question, the perimeter of a square is 30cm.

Then, by applying the formula of the square we get

P= 4* side

30= 4* side

30/4 =side

Side=5cm

After that we calculate the area of the square by applying the formula:

Area= side*side* Area= 5*5

Area= 25cm2

**How to calculate the area of the square when the diagonal of a square is given?**

The formula which is used to calculate the area of a square, when the diagonal of

square is given=

A= (diagonal* diagonal)/2

Let us clear this with the help o**f some examples:**

**Example 1: **Calculate the area of the square when the diagonal of a given square is 4cm

**Solution:**

According to the question, the diagonal of the square is 4cm.

Then, by applying the formula of diagonal of a square, we get:

A=(diagonal*diagonal)/2 A= (44)/2

A=16/2

A=8cm2

So, the area of the square whose diagonal given is 4cm is 8cm2

**Example 2: **Calculate the area of a square whose diagonal is the 14cm2

**Solution:**

Now, the diagonal of a given square is 14cm2

And we can calculate the area of the square by applying the formula of diagonal of

square:

A= (diagonal*diagonal)/2 Then, A=(14*14)/2

A= (196)/2

A= 98cm2

So, from the above calculations and examples, we learn about the area of a square and how we can calculate the area of a square by different dimensions. Like, firstly we calculate the area of the square by applying the normal formula of area of the square then we learned to calculate the area of the square when the perimeter of the square is given and at last we learn to calculate the area of a square with the help of the diagonal of a given square.

Also, Check the Area of a Triangle.

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