Square with Side 4.5: Comparing Perimeter vs Area Measurements

Square Measurements with Numerical Comparison

Look at the square below:

4.54.54.5

Is the value of the perimeter of the square greater than 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 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
00:10 Let's substitute appropriate values and solve for the perimeter
00:13 This is the square's perimeter
00:17 Let's use the formula for calculating square area (side squared)
00:21 Let's substitute appropriate values and solve for the area
00:29 The square's perimeter is less than its area
00:34 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:

4.54.54.5

Is the value of the perimeter of the square greater than the area 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=4.52=20.25 A=4.5^2=20.25

We calculate the perimeter of the square:

4.5×4=18 4.5\times4=18

Therefore, the perimeter is not greater than the area.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Formula Rule: Area equals side squared, perimeter equals side times four
  • Calculate Method: Area = 4.52=20.25 4.5^2 = 20.25 , Perimeter = 4.5×4=18 4.5 \times 4 = 18
  • Compare Values: Check which is greater: 20.25 > 18, so area wins ✓

Common Mistakes

Avoid these frequent errors
  • Mixing up area and perimeter formulas
    Don't use side × 4 for area or side² for perimeter = completely wrong calculations! This reverses the formulas and gives opposite conclusions. Always remember: area uses squaring (×itself), 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 area bigger than perimeter when the side is 4.5?

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When the side length is greater than 4, the area will always be larger than the perimeter! This happens because squaring a number bigger than 4 gives a result larger than multiplying it by 4.

What happens when the side length is exactly 4?

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When the side equals 4, both area and perimeter equal 16! This is the special case where 42=4×4 4^2 = 4 \times 4 .

Are there cases where perimeter is greater than area?

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Yes! When the side length is less than 4, the perimeter will be greater than the area. For example, if side = 2, then area = 4 but perimeter = 8.

Do I need to include units in my comparison?

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Be careful with units! Area has square units (like cm²) while perimeter has linear units (like cm). For comparison purposes, we just compare the numerical values.

How can I quickly tell which will be bigger without calculating?

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  • If side > 4: Area wins
  • If side = 4: They're equal
  • If side < 4: Perimeter wins

This rule works because we're comparing side² vs 4×side!

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