Question

Question
A trapezoid has a base of 10 inches, sides of 8 inches, and a top length of 4 inches. Suppose the trapezoid is dilated using a scale factor of 1/2 . What is the perimeter of the dilated trapezoid?(1 point)
Responses

15 inches
15 inches

11 inches
11 inches

60 inches
60 inches

30 inches
30 inches
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Answer 1

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**.