To find the area of the dilated square, we can start by calculating the area of the original square.
The area \( A \) of a square is given by the formula:
\[ A = \text{side length}^2 \]
For the original square with a side length of 3 inches:
\[ A = 3^2 = 9 \text{ square inches} \]
Next, we dilate the square using a scale factor of 1.5. The side length of the dilated square will be:
\[ \text{new side length} = 3 \times 1.5 = 4.5 \text{ inches} \]
Now we can find the area of the dilated square:
\[ A_{\text{dilated}} = (4.5)^2 = 20.25 \text{ square inches} \]
Thus, the area of the dilated square is:
\[ \boxed{20.25} \text{ square inches} \]