~only answer if you know for sure~
- you-

3 yards by 9 yards is the original figure.

We can obviously say that the trapezoid falls into the Not Similar - Different Shape category since it is a trapezoid, and we were given a rectangle :P

The 6 yard by 3 yard falls into the category of Not similar - Different ratio of Side Lengths because  the original was 9 yards by 3 yards. And one side remained the same while the other went larger, so they are not in a ratio.

The 2 yard by 8 yard falls into the category of Not similar - Different ratio of Side Lengths because  2 yards by 8 yards can be simplified in a ratio of 1 to 4 while the original is 3 to 9 or 1 to 3

The 6 yard by 18 yard falls into the category of Similar because  6 yards by 18 yards can be simplified in a ratio of 1 to 3 and the original is 3 to 9 which can be simplified to 1 to 3

The 9 yard by 8 yard falls into the category of Not similar - Different ratio of Side Lengths because  9 yards by 18 yards can be simplified in a ratio of 1 to 2 while the original is 3 yards to 9 yards or 1 to 3.

The 1 yard by 3 yard falls into the category of Similar because  1 yards by 3 yards can be simplified in a ratio of 1 to 3 and the original is 3 yards to 9 yards which can be simplified to 1 to 3