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.(1 point) The area of the dilated square is square inches.

Answer 1

To find the area of the dilated square, we first need to determine the new side length after dilation.

The original square has a side length of 3 inches. When dilated by a scale factor of 1.5, the new side length \(s\) can be calculated as follows:

\[ s = \text{original side length} \times \text{scale factor} \] \[ s = 3 , \text{inches} \times 1.5 = 4.5 , \text{inches} \]

Now that we know the new side length, we can find the area \(A\) of the dilated square:

\[ A = \text{side length}^2 \] \[ A = (4.5 , \text{inches})^2 = 20.25 , \text{square inches} \]

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