Calculate the Area of a Square with Side Length 3: Visual Geometry Problem

Square Area Calculation with Side Length

Look at the square below:

333

What is the area of the square?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the area of the square
00:03 The length of the square's side according to the given data
00:07 Use the formula to calculate the square's area (side squared)
00:14 Substitute appropriate values and solve to find the area
00:20 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the square below:

333

What is the area of the square?

2

Step-by-step solution

The area of the square is equal to the side of the square raised to the second power.

That is:

A=L2 A=L^2

Since the diagram provides us with one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

A=32=9 A=3^2=9

3

Final Answer

9 9

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square equals side length squared (A=L2 A = L^2 )
  • Technique: Square the given side: 32=3×3=9 3^2 = 3 \times 3 = 9
  • Check: Count unit squares in diagram: 3 rows × 3 columns = 9 ✓

Common Mistakes

Avoid these frequent errors
  • Using perimeter formula instead of area formula
    Don't add the sides like 3 + 3 + 3 + 3 = 12! That gives you perimeter (distance around), not area (space inside). Always use A=L2 A = L^2 for square area, which means multiply the side by itself.

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 multiply 3 × 3 instead of adding the sides?

+

Area measures space inside the shape, not distance around it. Think of it as counting unit squares: you need 3 rows of 3 squares each, so 3 × 3 = 9 total squares!

What's the difference between area and perimeter?

+

Perimeter is the distance around the outside (3 + 3 + 3 + 3 = 12). Area is the space inside (3 × 3 = 9). Area uses square units like cm², while perimeter uses regular units like cm.

Do I always square the side length for any square?

+

Yes! The formula A=L2 A = L^2 works for any square, no matter what the side length is. If the side is 5, area is 25. If the side is 10, area is 100.

How can I visualize why it's 3²?

+

Imagine filling the square with unit squares (1×1 squares). You can fit 3 unit squares along each side, creating a 3 by 3 grid with 9 total unit squares inside!

What if the side length has decimals or fractions?

+

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

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Square for 9th Grade questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations