Like the Simpsons, I don't think the characters are meant to age....
Mr. Krabs's license ("Sleepy Time") would put him around his late 50's. "Mid-Life Crustacean" somewhat confirms this.
Well, "The Bully" indicated that Patrick had once gone to community college, which would probably put him in at least his 20's.
As with Spongebob (and here I think I'm echoing other threads, even comments I've made), I think the writers and producers purposely make it so that his age is a bit "blurry," for lack of a better word. He simulateneously possesses traits of both children and adults; the movie was, in part, playing on that deliberate uncertainty. The literature word for this is called
liminality. The closest word for liminality would be sort of an "in-between-ness," that is, Spongebob is sort of in-between childhood and adulthood (hope that made sense.)
And by saying he's "in-between childhood and adulthood," I
don't simply mean that he's an adolescent. It's just more complicated than that.
In the end, I don't think we're
meant to know his age; part of the point is to leave his age somewhat uncertain.