Square Geometry: Compare Area vs Perimeter of a 9-Unit Square

Square Properties with Area-Perimeter Comparison

Look at the square below:

999

Is the value of the area of the square greater than the perimeter of the square?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Is the area of the square greater than its perimeter?
00:09 We start with the length of one side of the square.
00:13 Remember, the perimeter is four times the side length.
00:16 Let's plug in the value for the side and solve for the perimeter.
00:21 Now we have the perimeter of the square.
00:24 Next, we'll find the area using the formula: side squared.
00:28 Substitute the values and solve to get the area.
00:34 Here, the area is greater than the perimeter.
00:38 And that's how we solve 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

Is the value of the area of the square greater than the perimeter of the square?

2

Step-by-step solution

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

Remember that the perimeter of the square is equal to the side of the square multiplied by 4.

We calculate the area of the square:

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

We calculate the perimeter of the square:9×4=36 9\times4=36

Therefore, the area is greater than the perimeter.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Square the side length to find area
  • Perimeter Formula: Multiply side by 4: 9×4=36 9 \times 4 = 36
  • Compare Values: Check which is larger: 81 > 36, so area wins ✓

Common Mistakes

Avoid these frequent errors
  • Confusing area and perimeter formulas
    Don't use side × 4 for area or side² for perimeter = completely wrong values! Area measures space inside (square units), perimeter measures distance around (linear units). Always remember: area = side², perimeter = 4 × side.

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 is the area 81 when the side is only 9?

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Area uses square units! When you calculate 92=9×9=81 9^2 = 9 \times 9 = 81 , you're counting 81 small squares that fit inside. It's much larger than the perimeter because area fills the entire space.

Will area always be bigger than perimeter for squares?

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Not always! For small squares like 1×1 or 2×2, the perimeter is actually larger. Try it: a 2×2 square has area = 4 and perimeter = 8. Area overtakes perimeter when sides are longer than 4 units.

How do I remember which formula is which?

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Think about what you're measuring: Area fills up the inside space (like carpet), so you multiply length × width. Perimeter goes around the outside edge (like a fence), so you add up all four sides.

What if I get confused about which is greater?

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Calculate both values first, then compare the numbers directly. Write them side by side: Area = 81, Perimeter = 36. Since 81 > 36, area is greater.

Do the units matter when comparing?

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Yes! Area uses square units (like cm²) while perimeter uses linear units (like cm). But for comparison questions, you just compare the numbers: 81 vs 36.

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