To find the surface area of the original figure before dilation, you can use the property that the surface area of a dilated figure is equal to the surface area of the original figure multiplied by the square of the scale factor.
Let \( S_o \) be the surface area of the original figure, and the scale factor \( k = 6 \). The surface area of the dilated figure (\( S_d \)) is given as 10,990.8 in².
The formula to relate the original surface area to the dilated surface area is:
\[ S_d = k^2 \times S_o \]
Substituting the known values into the formula:
\[ 10,990.8 = 6^2 \times S_o \]
Calculating \( 6^2 \):
\[ 6^2 = 36 \]
Now, substituting that back into the equation:
\[ 10,990.8 = 36 \times S_o \]
To find \( S_o \), divide both sides by 36:
\[ S_o = \frac{10,990.8}{36} \approx 305.3 \]
So the surface area of the original figure is approximately 305.3 in².
The correct response is 305.3 in.².