Frank draws a square that measure 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.

Question

The area of the dilated square is __ square inches.

Answer 1

To find the area of the dilated square, we can follow these steps:

1. Find the area of the original square: The area \( A \) of a square is calculated using the formula: \[ A = \text{side}^2 \] The original square has a side length of 3 inches. Thus, the area is: \[ A = 3^2 = 9 \text{ square inches} \]

2. Dilate the square: The dilation scale factor is 1.5. When we dilate a square, we multiply each side length by the scale factor. The new side length of the square after dilation will be: \[ \text{new side} = 3 \times 1.5 = 4.5 \text{ inches} \]

3. Calculate the area of the dilated square: Using the area formula again for the dilated square: \[ A_{\text{dilated}} = (\text{new side})^2 = (4.5)^2 \] To calculate \( (4.5)^2 \): \[ (4.5)^2 = 20.25 \]

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