Noun of Noun vs Noun Noun - difference

Hello.
I'd like to know about noun of noun vs noun noun.

For instance,
First, the perimeter of convex hull Vs convex hull perimeter
- I guess that may be the former is right. But I don't know why is it.

Second, the sum of the perimeters Vs sum perimeter
- It is also the right phrase may be former. But I don't know why is it.

Third, the sum of the perimeters of the convex hulls Vs the sum of the convex hull perimeters 
- This is very difficult question to me. The former has too many of, so it looks more complex than letter.
I guess former is right phrase. How about letter phrase?

Thank you.

Green - Best

Yellow - Okay

red - wrong

This is an interesting question, and the answer is....there is not a rule.

The only one that is wrong is the second one, and that is because "sum" is an example of a noun that normally only follows the "noun + of + noun" rule.  Also, you switched the order.  

http://english.stackexchange.com/questions/131240/noun-of-noun-vs-nounnoun

There is not a consistent pattern for which one to use.  It is all about what sounds correct.

If you have questions please let me know.