When a figure is dilated by a scale factor \( k \), the surface area of the dilated figure is proportional to the square of the scale factor. This means:
\[ \text{Surface Area of Dilated Figure} = k^2 \times \text{Surface Area of Original Figure} \]
In this case, the scale factor \( k \) is 6, so \( k^2 = 6^2 = 36 \).
Given that the surface area of the dilated figure is 10,990.8 in², we can set up the equation:
\[ 10,990.8 = 36 \times \text{Surface Area of Original Figure} \]
To find the surface area of the original figure, we can divide both sides of the equation by 36:
\[ \text{Surface Area of Original Figure} = \frac{10,990.8}{36} \approx 305.3 , \text{in}^2 \]
Therefore, the surface area of the original figure is approximately 305.3 in².
So the correct response is:
305.3 in.².