To find the perimeter of the dilated trapezoid, we first need to find the perimeter of the original trapezoid.
The original trapezoid has:
- Base (bottom side) = 10 inches
- Top side (top length) = 4 inches
- Two sides = 8 inches each
To calculate the perimeter of the original trapezoid, we add the lengths of all sides:
\[ \text{Perimeter} = \text{Base} + \text{Top side} + \text{Side 1} + \text{Side 2} \] \[ \text{Perimeter} = 10 + 4 + 8 + 8 = 30 \text{ inches} \]
Next, we apply the dilation with a scale factor of 12. When a shape is dilated, all linear dimensions are multiplied by the scale factor. Therefore, the perimeter of the dilated trapezoid will also be multiplied by the scale factor.
We calculate the perimeter of the dilated trapezoid as follows:
\[ \text{Perimeter of dilated trapezoid} = \text{Perimeter of original trapezoid} \times \text{scale factor} \] \[ \text{Perimeter of dilated trapezoid} = 30 \times 12 = 360 \text{ inches} \]
Thus, the perimeter of the dilated trapezoid is \( \boxed{360} \) inches.