Square Analysis: Comparing Perimeter vs Area in a 2-Unit Square

Perimeter vs Area with Unit Side Lengths

Look at the square below:

222

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
00:07 The perimeter of the square equals the sum of its sides
00:11 Let's substitute appropriate values and solve for the perimeter
00:14 This is the square's perimeter
00:17 Let's use the formula for calculating the square's area (side squared)
00:20 Let's substitute appropriate values and solve for the area
00:26 The square's perimeter is greater than its area
00:31 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:

222

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=22=4 A=2^2=4

We calculate the perimeter of the square:

2×4=8 2\times4=8

Therefore, the perimeter is greater than the area.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Square's area equals side length squared
  • Perimeter Formula: Square's perimeter equals 4 times side length
  • Check: Compare calculated values directly: 8 > 4 confirms perimeter exceeds area ✓

Common Mistakes

Avoid these frequent errors
  • Confusing area and perimeter formulas
    Don't use side × 4 for area or side² for perimeter = completely wrong calculations! This swaps the formulas and gives impossible comparisons. Always remember area uses squaring (side²) while perimeter uses multiplication by 4.

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 is the perimeter bigger than the area when the side is 2?

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This happens with small squares! When side length is small (like 1 or 2), multiplying by 4 gives a bigger result than squaring. Try it: 2×4=8 2 \times 4 = 8 vs 22=4 2^2 = 4 .

Will the perimeter always be bigger than the area?

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No! This only works for small squares. When the side length is greater than 4, the area becomes larger. For example, if side = 5: area = 25, perimeter = 20.

How do I remember which formula is which?

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

What units should I use for my answer?

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Since we're just comparing numbers, the units don't matter here. But remember: perimeter uses linear units (like cm) while area uses square units (like cm²).

Can I solve this without calculating both values?

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For comparison problems like this, it's best to calculate both values to be sure. Mental math works for simple cases, but showing your work prevents errors!

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