Calculate the Area of a Square with Side Length 9: Basic Geometry Problem

Square Area with Perfect Square Numbers

Look at the square below:

999

What is the area of the square?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the square's area
00:03 Square side length according to the given data
00:07 Use the formula to calculate square area (side squared)
00:12 Substitute appropriate values and solve to find the area
00:24 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:

999

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 drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

A=92=81 A=9^2=81

3

Final Answer

81 81

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square equals side length squared
  • Calculation: Side = 9, so Area = 9² = 81
  • Check: Count unit squares: 9 rows × 9 columns = 81 ✓

Common Mistakes

Avoid these frequent errors
  • Using perimeter formula instead of area formula
    Don't calculate 4 × 9 = 36! That gives you the perimeter (distance around), not the area (space inside). The perimeter formula adds all four sides, but area needs multiplication. Always use Area = side² for squares.

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 multiplying by 4?

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Area measures space inside the shape, not the distance around it. When you square 9, you're finding how many unit squares fit inside: 9 × 9 = 81 unit squares. Multiplying by 4 gives the perimeter!

What's the difference between 9² and 2 × 9?

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92 9^2 means 9 × 9 = 81, while 2 × 9 = 18. The exponent 2 tells you to multiply 9 by itself, not by 2!

How can I remember the area formula for squares?

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Think of it as "side times side" or imagine filling the square with unit squares. A 9×9 grid has 9 rows and 9 columns, so 9 × 9 = 81 total squares.

Is there a faster way to calculate 9²?

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Yes! Since 9² is a perfect square, you can memorize that 9² = 81. Other perfect squares to remember: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, etc.

What if the side length was a decimal like 9.5?

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The same formula works! 9.52=9.5×9.5=90.25 9.5^2 = 9.5 \times 9.5 = 90.25 . Just be extra careful with decimal multiplication.

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