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# Area of a Square- Definition, Formula, Examples

## 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. All sides of a square are equal in length.

Area of a square = s2

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 = (d2)/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:

1. Measure the length of one of the sides of the square. Make sure to use the same unit of measurement for all sides.
2. 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.
3. 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 cm2.

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 Length2) / 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 = s2,

the side length =  7 cm, into the formula:

A = (7 cm)2

A = 49 cm2

##### 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 = s2

A = (10 m)2

A = 100 m2

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 = s2 to find the area:

A = (8.49 cm)2

A ≈ 72.04 cm2

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

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