Solution:

What is the smallest perimeter a trapezoid can have

answer [1,1,2,1]

What is the smallest perimeter of a trapezoid with the non-parallel sides having different lengths

answer[1,1,3,2]

What are all of the trapezoids with a perimeter of 9

answer [1,2 3,3] [1,2 2,4] [1,3 2,3] [1,3 1,4] [2,3 2,2] [2,3 1,3] [2,4 1,2] [3,4 1,1]