I find it strange that Klasa is classroom, while it is not a declination of klas, it feels too close to be a that different. (At least I think of them as being very different things, one a physical room a building, the other a more abstract concept of knowledge transference)
Yes, "klasa" can mean both "classroom" and "class" in sense a group of pupils/students (it seems that in American English "class" is a synonym for "lesson" but in Polish you should use the word "lekcja") but also in more abstract sense like in "class of objects" or "social class".