To find the perimeter of the dilated trapezoid, we first need to determine the perimeter of the original trapezoid before dilation.
The perimeter \( P \) of a trapezoid is calculated as the sum of the lengths of all its sides. For the given trapezoid:
- Base 1 (bottom base) = 10 inches
- Base 2 (top base) = 4 inches
- Side 1 = 8 inches
- Side 2 = 8 inches
Now, we can find the perimeter of the original trapezoid:
\[ P = \text{Base 1} + \text{Base 2} + \text{Side 1} + \text{Side 2} \] \[ P = 10 + 4 + 8 + 8 \] \[ P = 30 \text{ inches} \]
Since the trapezoid is dilated with a scale factor of 12, the perimeter of the dilated trapezoid will be 12 times the perimeter of the original trapezoid:
\[ \text{Perimeter of dilated trapezoid} = 12 \times P \] \[ \text{Perimeter of dilated trapezoid} = 12 \times 30 \] \[ \text{Perimeter of dilated trapezoid} = 360 \text{ inches} \]
However, 360 inches is not one of the options provided. The original perimeter of 30 inches multiplied by the scale factor of 12 gives us 360 inches, which suggests that the answer does not match any of the provided options.
Please check the problem or provide the correct options, as the calculated perimeter of the dilated trapezoid is indeed 360 inches.
1 answer