Area of a Square – Definition, Formula, Examples
Updated on July 31, 2026
The area of a square is the amount of space inside it, and it equals the side length multiplied by itself: Area = side × side, or side². Area is always measured in square units, such as square centimeters (cm²) or square inches (in²). For a square with sides of 5 cm, the area is 5 × 5 = 25 cm².
Area is a cornerstone of elementary geometry. If your child wants extra practice connecting side length, perimeter, and area, a Brighterly geometry tutor can guide them.
What Is the Area of a Square?
The area of a square is the space enclosed by its four equal sides, measured in square units. Because all sides of a square are equal, knowing just one side is enough to find the area. If your measurements are in inches, the area is in square inches; if in centimeters, the area is in square centimeters.
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What Is the Area of a Square Formula?
The formula for the area of a square is Area = side × side, which is written as side². Since every side of a square is equal, multiplying one side by itself gives the total space inside. For example, a square with a side of 6 m has an area of 6² = 36 m².
How to Find the Area of a Square
You can find the area of a square from its side length, its perimeter, or its diagonal. The table below shows the formula for each case, so you can use whichever measurement you already have.
| If you know the… | Area formula |
| Side length (s) | A = s² |
| Perimeter (P) | A = (P ÷ 4)² |
| Diagonal (d) | A = d² ÷ 2 |
Area of a Square When the Side Is Given
When you know the side length, square it. For a square with a side of 5 cm, the area is 5 × 5 = 25 cm². This is the most direct way to find the area, and the one students use most often.
Area of a Square When the Perimeter Is Given
The perimeter of a square is the sum of its four equal sides, so dividing the perimeter by 4 gives one side. Then square that side. For a perimeter of 20 cm: 20 ÷ 4 = 5 cm, and 5 × 5 = 25 cm².
Area of a Square When the Diagonal Is Given
If you know the diagonal, use A = d² ÷ 2. For a diagonal of 6 cm, the area is 6² ÷ 2 = 36 ÷ 2 = 18 cm². This formula comes from the Pythagorean theorem, which relates a square’s side to its diagonal.
How to Calculate the Area of a Square (Step by Step)
- Identify what you know: the side, the perimeter, or the diagonal.
- If you have the perimeter or diagonal, first find the side length.
- Multiply the side by itself (or apply the matching formula).
- Write the answer in square units, such as cm² or in².
Solved Examples on the Area of a Square
Example 1: A square has a side of 9 in. Its area is 9 × 9 = 81 in².
Example 2: A square has a perimeter of 32 cm. One side is 32 ÷ 4 = 8 cm, so the area is 8 × 8 = 64 cm².
Example 3: A square has a diagonal of 10 cm. Its area is 10² ÷ 2 = 100 ÷ 2 = 50 cm².
Area and Square Worksheets
Put this into practice with related Brighterly worksheets:
Frequently Asked Questions About the Area of a Square
What Is the Formula for the Area of a Square?
The formula for the area of a square is Area = side × side, written as side². Because all four sides of a square are equal, you only need one side length to find the area. For example, a square with a side of 7 cm has an area of 7² = 49 cm². Area is always given in square units.
How Do You Find the Area of a Square From the Perimeter?
First, divide the perimeter by 4 to find one side, since a square has four equal sides. Then square that side length. For example, if the perimeter is 24 cm, one side is 24 ÷ 4 = 6 cm, and the area is 6 × 6 = 36 cm². This two-step method works for any square.
Why Is Area Measured in Square Units?
Area is measured in square units because it counts how many unit squares fit inside a shape. When you multiply a length by a length, the units multiply too — centimeters × centimeters become square centimeters (cm²). Square units show that area describes a two-dimensional space rather than a single distance.
What Is the Difference Between Area and Perimeter of a Square?
Area measures the space inside a square and uses square units, found with side². Perimeter measures the distance around the outside and uses regular length units, found by multiplying the side length by 4. For a square with a 5 cm side, the area is 25 cm², and the perimeter is 20 cm — different measurements of the same shape.
How Do You Find the Area of a Square With the Diagonal?
Use the formula A = d² ÷ 2, where d is the diagonal. For example, a square with an 8 cm diagonal has an area of 8² ÷ 2 = 64 ÷ 2 = 32 cm². This formula works because the diagonal splits the square into two right triangles, linking the diagonal to the side through the Pythagorean theorem.
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