To find the surface area of the original figure before dilation, we need to use the relationship between the surface area of a dilated figure and the scale factor. When a figure is dilated by a scale factor of \( k \), the surface area of the dilated figure is multiplied by \( k^2 \).
In this case, the scale factor \( k = 6 \). Therefore, the surface area of the dilated figure (10,990.8 in²) can be expressed in terms of the original surface area \( A \) as follows:
\[ \text{Surface Area of Dilated Figure} = k^2 \times \text{Surface Area of Original Figure} \]
Substituting in the known values:
\[ 10,990.8 = 6^2 \times A \]
Calculating \( 6^2 \):
\[ 6^2 = 36 \]
Now substituting this back in:
\[ 10,990.8 = 36 \times A \]
To find \( A \), divide both sides by 36:
\[ A = \frac{10,990.8}{36} \]
Calculating \( A \):
\[ A = 305.3 \text{ in}^2 \]
Thus, the surface area of the original figure is:
\(\boxed{305.3 \text{ in}^2}\) (Option A)
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