Calculate the Area of a Square with Side Length 6 Units

Square Area with Integer Side Length

Look at the square below:

666

What is its area?

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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)
00:11 Substitute appropriate values and solve to find the area
00:18 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:

666

What is its area?

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=62=36 A=6^2=36

3

Final Answer

36 36

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of a square equals side length squared
  • Calculation: Apply A=L2 A = L^2 where L = 6
  • Check: Verify 6 × 6 = 36 square units ✓

Common Mistakes

Avoid these frequent errors
  • Using perimeter formula instead of area formula
    Don't calculate 4 × 6 = 24! This gives you the perimeter (distance around the square), not the area (space inside). Always use A=L2 A = L^2 for square area.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

555

What is the area of the square equivalent to?

FAQ

Everything you need to know about this question

Why do I square the side length instead of just multiplying by 4?

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Multiplying by 4 gives you the perimeter (the distance around the outside). For area (the space inside), you need to multiply length × width, and since all sides are equal in a square, that's 6×6=62=36 6 \times 6 = 6^2 = 36 .

What's the difference between 36 and 36 square units?

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The number 36 is just a value, but 36 square units tells us we're measuring area. Always include units in your final answer - it shows you understand what you're calculating!

How do I remember the area formula for squares?

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Think of it as filling up the square with unit squares. With side length 6, you can fit 6 rows of 6 unit squares each, giving you 6×6=36 6 \times 6 = 36 total unit squares.

What if the side length was a decimal like 6.5?

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The same formula works! You'd calculate 6.52=6.5×6.5=42.25 6.5^2 = 6.5 \times 6.5 = 42.25 square units. The method never changes, just the arithmetic.

Can I use this formula for rectangles too?

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No! Rectangles have different length and width, so you use A=length×width A = length \times width . The L2 L^2 formula only works for squares because all sides are equal.

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