To find the surface area of the original figure before dilation, we can use the following relationship between the surface areas of the original figure and the dilated figure:
\[ \text{Surface Area of Dilated Figure} = k^2 \times \text{Surface Area of Original Figure} \]
where \( k \) is the scale factor of the dilation. In this case, the scale factor \( k \) is 6.
Given that the surface area of the dilated figure is \( 10,990.8 , \text{in}^2 \), we can set up the equation:
\[ 10,990.8 = 6^2 \times \text{Surface Area of Original Figure} \]
Calculating \( k^2 \):
\[ 6^2 = 36 \]
Now, we can rewrite the equation as:
\[ 10,990.8 = 36 \times \text{Surface Area of Original Figure} \]
To find the surface area of the original figure, we divide both sides by 36:
\[ \text{Surface Area of Original Figure} = \frac{10,990.8}{36} \]
Calculating the right-hand side:
\[ \text{Surface Area of Original Figure} = 305.25 , \text{in}^2 \]
Thus, the surface area of the original figure is \( \boxed{305.25} , \text{in}^2 \).