Area of Square

The area of a square is a basic but important concept in geometry. It measures the space enclosed within the four equal-length sides of a square. Since all sides are equal, calculating its area is straightforward, making it easier than most other shapes. You’ll often see the area of a square in math problems related to measurement, real estate planning, architecture, engineering, and school-level math.  

In simple terms, the area of a square is the total space or surface that lies within the boundaries of the square.  

 

Table of Contents

• What is the Area of a Square?
• Area of Square Formula
• How to Find the Area of a Square
• Area of Square Using Diagonal
• Area of Square with Diagonal
• Solved Examples
• Real-Life Applications of Area of Square
• Conclusion
• FAQs on Area of Square

 

What is the Area of a Square?  

Let’s look at what is the area of a square is in more detail.  

A square is a 2D closed figure with four equal sides and four 90-degree angles. When we refer to what is the area of a square, we mean the amount of flat space that it covers. This is always expressed in square units like square centimeters (cm²), square meters (m²), square inches (in²), and so on.  

So, what is the area of a square?  

It is the number of square units that fit inside the boundaries of the square.  

For example:

If one side of a square is 5 meters, the area of the square = 5 × 5 = 25 m². This means 25 squares of 1m × 1m can fit inside the square.  

Understanding the area of a square helps us solve real-life problems, such as figuring out how much carpet is needed for a square room or how much land a square plot covers.  

 

Area of Square Formula  

To calculate the area of a square, we use a simple formula. Because all sides are equal, we don’t need different values for length and width like we do for rectangles.  

The area of square formula is:

Area = side × side  

Or simply:  

Area = side²  

Where “side” represents the length of one side of the square.  

So, if you know the side of the square, plug it into the area of square formula to get the answer instantly.

Example:  

If the side of a square is 9 cm, then  

Area = 9 × 9 = 81 cm².  

The area of square formula is one of the easiest to remember and use.  

 

How to Find the Area of a Square?  

If you're wondering how to find the area of a square, the first step is to determine whether you have the side length or the diagonal.  

Method 1: When Side is Given  

This is the most direct method. Use the area of square formula:  

Area = side × side   

or  

Area = side²  

Example:  

Side = 6 meters  

Area = 6 × 6 = 36 m².  

This is the simplest answer to how to find the area of a square.

 

Method 2: When Diagonal is Given  

Sometimes you have the diagonal of the square, not the side. In those cases, use the method for finding the area with the diagonal.  

Use the formula: Area = (1/2) × diagonal²

So, when someone asks how to find the area of a square and gives you the diagonal, this formula is perfect.

Example:
Diagonal = 10 cm
Area = (1/2) × 10² = 50 cm²

Both these techniques help answer how to find the area of a square depending on what is provided in the question.

 

Area of Square Using Diagonal  

Let’s explain the concept of area of square using diagonal in more depth.

Every square can be split into two right-angled triangles by its diagonal. According to the Pythagorean Theorem, in a right triangle:

Diagonal² = side² + side² = 2 × side²

Now rearrange the formula:

side² = (diagonal²)/2

But we know side² is the area of square, so:

Area of square using diagonal = (1/2) × diagonal²

This is especially helpful when the side of the square is not known but the diagonal is given.

Example:
If diagonal = 14 cm
Area = (1/2) × 14² = (1/2) × 196 = 98 cm²

So, when you are only given the diagonal, you can confidently use the area of square using diagonal formula.

 

Area of Square with Diagonal  

Let’s take another closer look at the area of square with diagonal.

We already derived that:

Area = (1/2) × diagonal²

This method is very useful in fields like engineering or architecture where diagonal measurements are often used.

Example:
Diagonal = 12 m
Area = (1/2) × 12² = (1/2) × 144 = 72 m²

So, if someone asks you to calculate the area of square with diagonal, this is the formula to use.

This method makes it easy to work with square shapes in real-life scenarios when only the diagonal is measurable.

 

Solved Examples

Example 1:
Question: A square has a side of 10 cm. What is the area of square?
Solution:
Area = side × side = 10 × 10 = 100 cm²
Answer: 100 cm²

 

Example 2:
Question: What is the area of a square if each side is 13 meters?
Solution:
Area = side² = 13 × 13 = 169 m²
Answer: 169 m²

 

Example 3
Question: A square has a diagonal of 14 cm. Find the area of square using diagonal.
Solution:
Area = (1/2) × diagonal² = (1/2) × 14² = (1/2) × 196 = 98 cm²
Answer: 98 cm²

 

Example 4
Question: Find the area of square with diagonal 20 m.
Solution:
Area = (1/2) × diagonal² = (1/2) × 20² = (1/2) × 400 = 200 m²
Answer: 200 m²

 

Example 5
Question: A square tile has a side of 25 cm. What is the area of square?
Solution:
Area = side × side = 25 × 25 = 625 cm²
Answer: 625 cm²

 

Real-Life Applications of Area of Square  

• Interior Design 
  If you want to lay carpet in a square room, measure the side and use the area formula to find out how much carpet you’ll need.  

• Agriculture 
  Farmers often need to calculate how much land they can use. For a square plot, the area = side × side gives them accurate results.  

• Art and Drawing
  Drawing a square frame or grid on a canvas uses the idea of what is the area of a square to understand space coverage.

• Construction 
  Engineers use both the area formulas based on side and diagonal to calculate the materials needed.  

• Technology 
  In screen design, if the screen is square and only the diagonal is known, use the area with diagonal formula to determine the screen size in inches².  

 

Formulas Table Summary  

 

 

Conclusion

The area of square is one of the most practical and easy-to-use formulas in geometry. Whether you're measuring land, designing art, or working with screens, understanding what is the area of a square is essential. Use the area of square formula when the side is known, and switch to the area of square using diagonal or area of square with diagonal method when only the diagonal is provided. With both formulas in your toolkit, you’ll be ready to solve any square area problem in school or real life.

 

Related Links

2D Shapes - Understand the different types of 2D shapes, their properties, and how they form the foundation of basic geometry.

Area of Trapezium - Learn how to calculate the area of a trapezium using formulas, with step-by-step examples and visual aids.

Area of a Triangle - Understand how to calculate the area of a triangle with easy methods.

Area and Perimeter - Learn how to find the area and perimeter of different shapes with examples.

 

Frequently Asked Questions on Area of Square

1. What is the formula for area of square?

Answer: The formula for the area of square is:
Area = side × side = s²

 

2. What is the area of a 4 cm square?

Answer: The area of a square with side 4 cm is:
Area = 4 × 4 = 16 cm²

 

3. What is the area and perimeter of a square?

Answer: If the side of a square is 's':
Area = s²
Perimeter = 4 × s

 

4. What is the area of the rectangle?

Answer: The area of a rectangle is:
           Area = length × breadth = l × b

 

5. What is the area of a cube?

Answer: A cube has 6 square faces. The surface area of a cube is:
          Area = 6 × side²

 

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