Question

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

15
11
60
30

Answer 1

To find the perimeter of the dilated trapezoid, we first need to find the perimeter of the original trapezoid before dilation.

The sides of the trapezoid are as follows:
- Base 1: 10 inches
- Base 2 (top): 4 inches
- Side 1: 8 inches
- Side 2: 8 inches

Now we calculate the perimeter of the original trapezoid:

\[
\text{Perimeter} = \text{Base 1} + \text{Base 2} + \text{Side 1} + \text{Side 2}
\]

Substituting in the values:

\[
\text{Perimeter} = 10 + 4 + 8 + 8 = 30 \text{ inches}
\]

Next, we apply the dilation using a scale factor of \( \frac{1}{2} \). Dilation affects all linear dimensions, including lengths. Thus, the new lengths after dilation will be:

- New Base 1 = \( 10 \times \frac{1}{2} = 5 \) inches
- New Base 2 = \( 4 \times \frac{1}{2} = 2 \) inches
- New Side 1 = \( 8 \times \frac{1}{2} = 4 \) inches
- New Side 2 = \( 8 \times \frac{1}{2} = 4 \) inches

Now, we calculate the perimeter of the dilated trapezoid:

\[
\text{New Perimeter} = \text{New Base 1} + \text{New Base 2} + \text{New Side 1} + \text{New Side 2}
\]

Substituting in the new lengths:

\[
\text{New Perimeter} = 5 + 2 + 4 + 4 = 15 \text{ inches}
\]

Thus, the perimeter of the dilated trapezoid is \( \boxed{15} \) inches.