To find the perimeter of the dilated trapezoid, we first need to calculate the perimeter of the original trapezoid.
The trapezoid has the following sides:
- Base 1 = 10 inches
- Base 2 = 4 inches
- Side 1 = 8 inches
- Side 2 = 8 inches
The perimeter (P) of the trapezoid can be calculated as follows:
\[ P = \text{Base 1} + \text{Base 2} + \text{Side 1} + \text{Side 2} \] \[ P = 10 + 4 + 8 + 8 = 30 \text{ inches} \]
Now, we will apply the dilation using a scale factor of \( \frac{1}{2} \).
The new perimeter (P') of the dilated trapezoid is calculated by multiplying the original perimeter by the scale factor:
\[ P' = P \times \frac{1}{2} = 30 \times \frac{1}{2} = 15 \text{ inches} \]
Thus, the perimeter of the dilated trapezoid is 15 inches.
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