The best bet is to go in to the SCHOA office and have the add-on or shed checked out by a compliance officer. Many additions are within CC&R statutes.
When I was buying I had read that a shed is allowed if attached to the house. It cannot be freestanding.
This has been a long standing battle at SCHOA. They've been telling people sheds are illegal unless as C pointed out, attached to the existing house and made to look like it is part of the house. That said, folks have been drifting from that by putting up "garages" that must meet the setback requirements in the CC&R's. It gets more convoluted with some folks who have had sheds that have been there for more than 7 years with no complaints and hence SCHOA attorneys used to tell them they should be grandfathered until they are sold. It's one of the things SCHOA does when a change of ownership takes place and the document fee is paid, they go do an inspection to insure there are no surprises to the new owner. Then of course there's the whole argument if a violation is hidden behind a wall and can't be seen, is it still a violation? Any takers on that one?
I believe if I have a 6' block wall, I should be able to have a shed. 95% or more will be out of sight, and some folks need the extra storage for garden supplies, pool supplies, other items needed around the yard. Some of the chemicals used to kill the weeds and keep them under control are noxious, and are best not stored under the patio, especially if you have pets. If you don't have a barrier wall or fence, THEN is when the shed prohibition should be imposed. just my opinion of course. NO, we don't have a shed behind our house.
