## Square Definition

A square is a four-sided polygon with all sides equal in length and all angles equal to 90 degrees. The area of a square is the measure of the region enclosed by the square.

### Properties of a Square

- All sides of a square are equal in length.
- The internal angles of a square are all 90 degrees.
- The diagonals of a square are equal in length and intersect each other at 90 degrees.
- The perimeter of a square is the sum of all four sides.

## What is the Area of Square?

The area of a square is the measure of the region enclosed by the square. To calculate the area of a square, we simply **multiply the length of one side by itself. A**ll sides of a square are equal in length.

**Area of a square = s ^{2}**

where s is the length of one side of the square.

**Area of a square using diagonals**

The area of a square can also be found using the length of the diagonal. The diagonal of a square can be found using the Pythagorean theorem. If a square has a diagonal length of d then:

**Area of a square = (d ^{2})/2**

, where d is the diagonal length.

## How to Find the Area of a Square?

To find the area of a square, you can use the following formula:

Area of a Square = (Side Length)^{2}

Here are the steps to find the area of a square:

- Measure the length of one of the sides of the square. Make sure to use the same unit of measurement for all sides.
- Square the length of one of the sides of the square. To do this, multiply the side length by itself.
**For example**, if the side length of the square is 5 cm, you would calculate 5 x 5 = 25. - Write your answer with the correct units. Since area is measured in square units, you should write your answer as a squared unit. For example, if the side length of the square is 5 cm, the area of the square would be 25 square centimeters or 25 cm
^{2}.

Alternatively, you can find the area of a square using the length of its diagonal. Here is the formula to find the area of a square using the diagonal:

Area of a Square = (Diagonal Length^{2}) / 2

## Area of a Square Formula Examples

**Example 1: Find the area of a square with a side length of 7 cm.**

**Solution:** Using the formula A = s^{2},

the side length = 7 cm, into the formula:

A = (7 cm)^{2}

A = 49 cm^{2}

**Example 2: Find the area of a square with a side length of 10 meters.**

**Solution**: Substitute the side length of 10 meters into the formula:

the formula A = s^{2}

A = (10 m)^{2}

A = 100 m^{2}

Therefore, the area of the square is 100 square meters.

**Example 3: Find the area of a square with a diagonal length of 12 cm.**

**Solution:** To use the formula that involves the diagonal length, we need to first find the length of the side of the square. **Using the Pythagorean theorem**, we can calculate the length of the side:

Side Length = Diagonal Length / √2

Side Length = 12 cm / √2

Length ≈ 8.49 cm

Now that we know the side length, we can use the formula A = s^{2} to find the area:

A = (8.49 cm)^{2}

A ≈ 72.04 cm^{2}

Therefore, the area of the square is approximately 72.04 square centimeters.