# Area of Square

A square is a closed figure on a 2D plane that has four parallel sides. The property of the square is that all the sides (breadth and length) must have equal length. In a square, each angle is of 90�.

In this section, we will learn area of square formula, and how to find area of a square.

### Area of Square

The area is the region covered by the four-sides. In other words, the number of square units it takes to fill a square completely.

In the following image, we have divided a square into five rows and five columns. It makes the multiple small squares that completely fills the square. Hence 25 small squares represent the area of the square.

### Area of Square Formula

To calculate the area of a square, multiply the base to itself. In short, the square of the side is the area of the square.

Where a is the side of a square whose length is a.

#### When the diagonal is given

We can also calculate the area of a square if the length of the diagonal is given. The area is half the product of the diagonals. Both the diagonals are equal length.

Where d is the length of either diagonal.

### Derivation

Consider a square as a rectangular shape whose length is l and breadth are b. According to the area of rectangle formula:

A = l*b

Where,

• A is the area
• l is length

Suppose that a side of a square is a. Then the area of the square will be:

A = a*b

We know that all sides of the square are equal length. Then,

A = a*a

A = a2

### Examples

Example 1: Find the area of a square whose side length is 12 cm.

Solution:

We have given that a side of the square is 12 cm.

We know that

Area of square (A) = a2

A = 122= 144 cm2

The area of the square is 144 cm2.

Example 2: The perimeter if a square is 24 yd, calculate the area of the square.

Solution:

Given, perimeter (P) = 24 yd

We know that

Perimeter of the square (P) = 4a

Where a is the length of the side.

Putting the value of P in the above formula we get:

24 = 4a
a = 24/4
a = 6 yd

We know that,

Area of square (A) = a2

Substitute value and simplify, we get:

A = 6*6 = 36 yd2

The area of the square is 36 yd2.

Example 3: Find the area of the given square.

Solution:

Given, length of diagonal (d) = 6 m

We know that,

Area of square (A) = d2/2

Putting the value of d in the above formula, we get:

A = (6)2/2

A = 36/2

A = 18 m2

The area of the square is 18 m2.

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