What is the smallest length marked on a 12-inch ruler?

Not all 12-inch rulers are the same. 

I have one with no marks smaller than 1/4 inch, and I have another one
with the first inch marked in 64ths of an inch.

This depends on the ruler. Some rulers show only inches, in which case the smallest length would be one length. Some even mark half, quarter, eighth, etc. inches so those would be even smaller. However, the standard 12 inch ruler will have marks as small as sixteenth inches. Therefore, the smallest length would be 1/16 inch.

You have 2 sides that are 2 cms and you have 6 sides that are 1/2 cm and you have 4 sides that are 1 cm. the smallest sides are 1/2 the medium sized sides are 1 and the smallest are 1/2. so to find the perimeter you have to add them all up together so your answer will be 11 cm's