Square is a regular quadrilateral. Here in the case of square its length and breadth called sides are equal to each other. Each of its angle is right angle ([latex]90^circ[/latex]). Diagonals of square are equal and bisect each other at right angle. Opposite sides of square are parallel to each other. Square is a four-sided polygon, which has all its sides equal in length. It is also a type of quadrilateral.

In the given figure above all sides are equal and each angle is right angle.

A square can also be defined as a rectangle where two opposite sides have equal length.

Area of  Square

Area of a square is the number of unit squares needed to fill in a square. It is simply defined as the area or the space occupied by it. Area is calculated in square units i.e. square centimeters, square meters, square inch, square feet etc or simply square units.

Area of Square Formula

Area of square can be calculated in following three different ways depending on the given values:

1. Area of square using sides
2. Area of square using diagonals
3. Area of square using perimeter

Now let us discuss all the methods in detail.

Area of Square using Sides

We can find the area of square when the side of square is given. To find area just square the value of side.

So Area of Square = [latex]{(side)}^2[/latex] i.e. side x side

Now let us understand the formula with examples:

Example 1: Find the area of a square sheet with a side of 12 cm.

Solution:

Side of square sheet given = 12 cm.

Area of Square = [latex]{(side)}^2[/latex]

so the area of square sheet = [latex]{(12)}^2[/latex]

= 12 x 12 [latex]{cm}^2[/latex]

= 144 [latex]{cm}^2[/latex]

Example 2: Find the area of a square whose side is 15 units.

Solution:

Side of square given = 15 units.

Area of Square = [latex]{(side)}^2[/latex]

so the area of square = [latex]{(15)}^2[/latex] square units

= 15 x 15 square units

= 225 square units

Area of Square using Diagonals

We can also find the area of square if its diagonals is given. Now we know that diagonals of square are equal and bisect each other at right angle. To get the area of square take the square of the diagonal and divide it by 2.

So, Area of Square = [latex]\frac{Diagonal^2}{2}[/latex]

Now let us understand the formula with examples:

Example 1: Find the area of a square whose diagonal is 20 cm.

Solution:

Diagonal of square given = 20 cm.

Area of Square = [latex]\frac{Diagonal^2}2[/latex]

= [latex]\frac{20^{2}}{2}[/latex]

= [latex]\frac{20 \times 20}{2}[/latex]

= [latex]\frac{400}{2}[/latex]

= 200 [latex]{cm}^2[/latex]

Example 2: What is the area of a square whose diagonal is 12 m long ?

Solution:

Area of Square = [latex]\frac{Diagonal^2}2[/latex]

= [latex]\frac{12^{2}}{2}[/latex]

= [latex]\frac{12 \times 12}{2}[/latex]

= [latex]\frac{144}{2}[/latex]

= 72 [latex]{m}^2[/latex]

Area of Square using Perimeter

We can also find the area of square if its perimeter is given. As we know all sides of square are equal. Thus perimeter of square is 4 times the side of square. To get the area of square divide the given perimeter by 4 and then multiply the result with itself.

So, Area of Square = [latex]{(\frac{Perimeter}4)}^2[/latex]

Now let us understand the formula with examples:

Example 1: Find the area of a square whose perimeter is 80 cm.

Solution:

Perimeter of square given = 80 cm

Area of square = [latex]{(\frac{Perimeter}4)}^2[/latex]

= [latex]{(\frac{80}4)}^2[/latex]

= [latex]{(20)}^2[/latex]

= [latex]{20 \times 20}[/latex]

= 400 [latex]{cm}^2[/latex]

Example 2: Find the area of a square whose perimeter is 32 m.

Solution:

Perimeter of square given = 32 m

Area of square = [latex]{(\frac{Perimeter}4)}^2[/latex]

= [latex]{(\frac{32}4)}^2[/latex]

= [latex]{(8)}^2[/latex]

= [latex]{8 \times 8}[/latex]

= 64 [latex]{m}^2[/latex]

Examples of Sqaure

There are many examples of square shaped planes like square shaped field, square shaped play ground, square shaped sheet etc.

This concludes the topic how to find area of square. Students are advised to practice more questions to clear the concept.