Frank draws a square that measures 3 inches on each side. then, he dilates the square using a scale factor of 1.5. what is the area of the dilated square? use a decimal response if necessary.

Answer 1

To find the area of the dilated square, we start with the original square that has a side length of 3 inches.

1. Calculate the area of the original square: \[ \text{Area} = \text{side}^2 = 3 , \text{inches} \times 3 , \text{inches} = 9 , \text{square inches} \]

2. Apply the dilation with a scale factor of 1.5. The new side length of the dilated square is: \[ \text{New side length} = 3 , \text{inches} \times 1.5 = 4.5 , \text{inches} \]

3. Calculate the area of the dilated square: \[ \text{Area} = \text{New side}^2 = 4.5 , \text{inches} \times 4.5 , \text{inches} = 20.25 , \text{square inches} \]

Thus, the area of the dilated square is \( \boxed{20.25} \) square inches.