Look at the square below:
Is the value of the perimeter of the square greater than the area of the square?
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Look at the square below:
Is the value of the perimeter of the square greater than the area of the square?
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:
We calculate the perimeter of the square:
Therefore, the perimeter is not greater than the area.
No
Look at the square below:
What is the area of the square?
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.
When the side equals 4, both area and perimeter equal 16! This is the special case where .
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.
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.
This rule works because we're comparing side² vs 4×side!
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