To find the area of the dilated square, we first need to determine the dimensions of the original square and then calculate the dimensions after dilation.
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Original Square: The side length of the original square is 3 inches.
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Area of the Original Square: The area \( A \) of a square is given by the formula: \[ A = \text{side length}^2 \] Thus, the area of the original square is: \[ A = 3^2 = 9 \text{ square inches} \]
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Dilation: Frank dilates the square with a scale factor of 1.5. The new side length \( s' \) of the dilated square is calculated as follows: \[ s' = \text{original side length} \times \text{scale factor} = 3 \text{ inches} \times 1.5 = 4.5 \text{ inches} \]
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Area of the Dilated Square: Now, we can calculate the area of the dilated square with the new side length: \[ A' = (s')^2 = (4.5)^2 \] Calculating \( (4.5)^2 \): \[ (4.5)^2 = 20.25 \text{ square inches} \]
Thus, the area of the dilated square is \(\boxed{20.25}\) square inches.
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