To find the perimeter of the dilated trapezoid, we first need to calculate the original perimeter of the trapezoid.
The perimeter \( P \) of the original trapezoid can be calculated using the lengths of all sides:
\[ P = \text{base} + \text{side 1} + \text{side 2} + \text{top} \]
Plugging in the values:
\[ P = 10 \text{ inches} + 8 \text{ inches} + 8 \text{ inches} + 4 \text{ inches} = 10 + 8 + 8 + 4 = 30 \text{ inches} \]
Next, we apply the dilation with a scale factor of 12. The new perimeter \( P' \) of the dilated trapezoid will be:
\[ P' = \text{scale factor} \times P = 12 \times 30 \text{ inches} = 360 \text{ inches} \]
None of the responses listed match this calculation exactly.
However, if the problem only requires the perimeter of the original trapezoid rather than the dilated one, the perimeter remains at:
\[ 30 \text{ inches} \]
Thus, if the question is strictly about the original trapezoid and clarifies nothing about dilation, the perimeter is \( 30 \) inches. If it's indeed asking about the perimeter post-dilation, it would be \( 360 \) inches, which is not provided in the options.
If you have to choose from the available responses regarding the original trapezoid, the answer is:
30 inches.