When a three-dimensional shape, such as a rectangular prism, is dilated, the surface area is affected by the square of the scale factor.
Given:
- Original surface area = \( 4 , \text{in}^2 \)
- Scale factor = \( 3 \)
The formula for the surface area of the dilated shape is:
\[ \text{New Surface Area} = \text{Original Surface Area} \times (\text{Scale Factor})^2 \]
Substituting the known values:
\[ \text{New Surface Area} = 4 \times 3^2 = 4 \times 9 = 36 , \text{in}^2 \]
Therefore, the surface area of the new dilated rectangular prism is \( \boxed{36} , \text{in}^2 \).