To find the area of the dilated square, we first need to calculate the dimensions of the square after dilation.
The original square has a side length of 3 inches. When we dilate the square using a scale factor of 1.5, the new side length \( L \) can be calculated as follows:
\[ L = 3 \text{ inches} \times 1.5 = 4.5 \text{ inches} \]
Next, we calculate the area \( A \) of the dilated square using the formula for the area of a square:
\[ A = L^2 = (4.5 \text{ inches})^2 \]
Calculating that gives:
\[ A = 20.25 \text{ square inches} \]
Therefore, the area of the dilated square is \( 20.25 \) square inches.