Look at the square below:
Is the value of the perimeter of the square greater than its area?
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Look at the square below:
Is the value of the perimeter of the square greater than its area?
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 greater than the area.
Yes
Look at the square below:
What is the area of the square?
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: vs .
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.
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).
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).
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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