Calculate the Area of a Square with Side Length 5

Square Area with Side Length Formula

Look at the square below:

555

What is the area of the square equivalent to?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's find the area of this square.
00:07 We use the formula: area equals side times side. That's side, squared.
00:15 Next, we'll substitute the value of the side, and then solve for the area.
00:27 And there you have it! That's how to find the area of a square.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the square below:

555

What is the area of the square equivalent to?

2

Step-by-step solution

The area of a square is equal to the square of its side length.

In other words:

S=a2 S=a^2

Since in the diagram we are given one side of the square, and in a square all sides are equal to each other, we will solve for the area of the square as follows:

S=52=25 S=5^2=25

3

Final Answer

25 25

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square equals side length squared: A=s2 A = s^2
  • Technique: Substitute side length: A=52=25 A = 5^2 = 25
  • Check: Count unit squares or verify 5×5=25 5 \times 5 = 25

Common Mistakes

Avoid these frequent errors
  • Adding side length instead of squaring
    Don't calculate 5 + 5 = 10 for area! This gives perimeter, not area, and is way too small. Always multiply side by itself: 52=5×5=25 5^2 = 5 \times 5 = 25 .

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

111111

What is the area of the square?

FAQ

Everything you need to know about this question

Why do I square the side length instead of just doubling it?

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Area measures the space inside the square. When you have a 5×5 square, you're filling it with 25 unit squares (5 rows of 5). Doubling gives you perimeter, which is the distance around the square.

What's the difference between area and perimeter?

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Area is the space inside (measured in square units like cm²). Perimeter is the distance around the outside (measured in linear units like cm). For this square: Area = 25, Perimeter = 20.

Do I always use the same formula for any square?

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Yes! The formula A=s2 A = s^2 works for any square, no matter the size. Just substitute your side length for 's' and square it.

How can I visualize why it's 5²?

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Imagine filling the square with small unit squares. You'd have 5 rows with 5 squares in each row. That's 5×5=25 5 \times 5 = 25 total unit squares!

What if the side length is a decimal or fraction?

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The same formula works! Just square whatever number you have. For example, if the side is 2.5, then A=2.52=6.25 A = 2.5^2 = 6.25 .

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