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?
Let's remember that the area of the square is equal to the side of the square raised to the second power.
Also, the perimeter of the square is equal to the side 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 of the square.
Yes
Look at the square below:
What is the area of the square equivalent to?
This happens with small squares! When the side length is small, the perimeter (12) grows slower than area would for larger squares. Try a 5×5 square: area = 25, perimeter = 20 - now area is bigger!
No! It depends on the side length. For squares with sides less than 4 units, perimeter > area. For sides greater than 4 units, area > perimeter. At exactly 4 units, they're equal!
Think about what you're measuring: Area fills the inside space (like tiles), so you multiply length × width = side². Perimeter goes around the edge (like a fence), so you add all 4 sides = 4 × side.
For a 3-unit square: area is 9 square units and perimeter is 12 units. Area always uses square units because you're measuring a flat space!
You could set up the inequality: where s = 3. But it's usually easier and clearer to just calculate both values and compare them directly.
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