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