When a three-dimensional object, such as a rectangular prism, is dilated by a scale factor \( k \), the surface area of the object is affected by the square of that scale factor.
In this case, the scale factor is \( k = 3 \). Therefore, the new surface area can be calculated using the formula:
\[ \text{New Surface Area} = \text{Original Surface Area} \times k^2 \]
Substituting in the values:
\[ \text{New Surface Area} = 4 , \text{in}^2 \times (3^2) = 4 , \text{in}^2 \times 9 = 36 , \text{in}^2 \]
Thus, the surface area of the new dilated rectangular prism is \( 36 , \text{in}^2 \).