To determine the ratio of the perimeters of two similar trapezoids given their side-length ratio, we start by understanding a key property of similar figures:
For any two similar figures, the ratio of any two corresponding lengths (such as the side lengths) is the same throughout the figures. This property also applies to other linear measures such as the perimeters.
Given the side-length ratio of the two similar trapezoids is [tex]\(\frac{1}{4}\)[/tex], the ratio of their corresponding side lengths is [tex]\(\frac{1}{4}\)[/tex].
Since the perimeter of a figure is essentially the sum of its side lengths, the ratio of the perimeters will be the same as the ratio of the corresponding side lengths. Hence, the ratio of the perimeters of the two similar trapezoids is also [tex]\(\frac{1}{4}\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{\frac{1}{4}}
\][/tex]
