To find the surface area of the original figure before dilation, we can use the relationship between the surface areas of similar figures and the square of the scale factor. Specifically, if a figure is dilated by a scale factor of \( k \), the surface area of the dilated figure \( A' \) is related to the surface area of the original figure \( A \) by the formula:
\[ A' = k^2 \cdot A \]
In this case, the scale factor \( k \) is 6, and the surface area of the dilated figure \( A' \) is 10,990.8 in². Let's set up the equation:
\[ 10,990.8 = 6^2 \cdot A \] \[ 10,990.8 = 36 \cdot A \]
Now, we can solve for \( A \) by dividing both sides by 36:
\[ A = \frac{10,990.8}{36} \]
Calculating that:
\[ A = 305.25 \text{ in}^2 \]
Thus, the surface area of the original figure is 305.25 in².