To find the area of a square given its perimeter, you can use the relationship between the perimeter and the side length of the square.
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The formula for the perimeter \( P \) of a square is given by: \[ P = 4s \] where \( s \) is the length of one side of the square.
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Given that the perimeter is 36 cm, you can find the side length: \[ 36 = 4s \] Dividing both sides by 4: \[ s = \frac{36}{4} = 9 \text{ cm} \]
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Now, to find the area \( A \) of the square, use the formula: \[ A = s^2 \] Substituting the value of \( s \): \[ A = 9^2 = 81 \text{ cm}^2 \]
Therefore, the area of the square with a perimeter of 36 cm is \( 81 , \text{cm}^2 \).
So, filling in the table:
- For a perimeter of 36 cm, the area is \( 81 , \text{cm}^2 \).
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