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