Square Geometry: Compare Perimeter and Area of 10-Unit Square

Square Properties with Numerical Comparison

Look at the square below:

101010

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is the perimeter of the square greater than its area?
00:03 Side length according to the given data
00:06 The perimeter of the square equals the sum of its sides
00:12 Let's substitute appropriate values and solve to find the perimeter
00:15 This is the perimeter of the square
00:20 Let's use the formula for calculating the area of a square (side squared)
00:26 Let's substitute appropriate values and solve to find the area
00:35 The perimeter of the square is less than its area
00:40 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the square below:

101010

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

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=102=100 A=10^2=100

We calculate the perimeter of the square:

10×4=40 10\times4=40

Therefore, the perimeter is not greater than the area.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Square area equals side length squared (s²)
  • Perimeter Formula: Square perimeter equals 4 times side length: 4×10 = 40
  • Check: Compare calculated values: Area 100 > Perimeter 40 ✓

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! This mixes up two different measurements with different units. Always remember: area uses side² (square units), perimeter uses 4×side (linear units).

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 100 when the side is only 10?

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Because area measures square units! When you multiply 10×10, you're counting how many unit squares fit inside. The area 102=100 10^2 = 100 square units is much larger than the perimeter of 40 linear units.

How can I remember which formula is which?

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Think about what you're measuring: Perimeter is the distance around the outside (add all 4 sides), while area is the space inside (multiply length × width).

Will the area always be bigger than the perimeter?

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Not always! For small squares with sides less than 4 units, the perimeter is actually larger than the area. Try a 2×2 square: area = 4, perimeter = 8!

What units should I use for my answer?

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Area uses square units (like cm², m²), while perimeter uses linear units (like cm, m). Since this problem asks for comparison, you can work with just the numbers: 100 vs 40.

Do I need to show both calculations in my work?

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Yes! Always calculate both the area and perimeter separately, then compare the results. This shows you understand both formulas and can make the comparison accurately.

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