Only you can tell if the pergola is common property or not and you can do that by looking at the original strata plan and any amendments made to it by by-laws and special resolutions since it was drawn up. It may, for instance, have been erected under a special resolution by-law, it could have been there as part of the building, or it could have been installed without permission (which means it is probably common property now).
If the building is older then 30 years, there's a very good chance that it's not common property but we can't tell if you can't. Check with your strata manager or look at the documents that came with the unit purchase.
However, if you give us more detail we may be able to hazard a guess.