To find the perimeter of the dilated trapezoid, we first need to calculate the perimeter of the original trapezoid.
The original trapezoid has the following dimensions:
- Base (bottom) = 10 inches
- Top = 4 inches
- Side 1 = 8 inches
- Side 2 = 8 inches
Now we calculate the perimeter of the original trapezoid:
\[ \text{Perimeter} = \text{Base} + \text{Top} + \text{Side 1} + \text{Side 2} \]
Substituting the values:
\[ \text{Perimeter} = 10 + 4 + 8 + 8 = 30 \text{ inches} \]
Next, since the trapezoid is dilated using a scale factor of \( \frac{1}{2} \), we compute the perimeter of the dilated trapezoid. The perimeter of a figure is also scaled by the same factor when the figure undergoes dilation. Therefore, we multiply the original perimeter by \( \frac{1}{2} \):
\[ \text{Perimeter of dilated trapezoid} = \text{Original Perimeter} \times \frac{1}{2} = 30 \times \frac{1}{2} = 15 \text{ inches} \]
Thus, the perimeter of the dilated trapezoid is:
\[ \boxed{15 \text{ inches}} \]
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