When a three-dimensional shape, such as a rectangular prism, is dilated with a scale factor of \( k \), the surface area of the shape changes by a factor of \( k^2 \).
In this case, the scale factor is 3, so we will calculate \( k^2 \):
\[ k^2 = 3^2 = 9 \]
Now, to find the surface area of the new dilated prism, we multiply the original surface area by this factor:
\[ \text{New Surface Area} = \text{Original Surface Area} \times k^2 \]
Given that the original surface area is \( 4 , \text{in}^2 \):
\[ \text{New Surface Area} = 4 , \text{in}^2 \times 9 = 36 , \text{in}^2 \]
Thus, the surface area of the new dilated rectangular prism is \( 36 , \text{in}^2 \).