I got in trouble for doing my homework at school, how do I address the adult about it?

I am an eight grader in middle school, during recess we are allowed to go to recess play games and crap. Or, you can go the library to do homework. Every couple of days, the library will be closed so I do my homework in a doorway next to my locker. Some people sit on the floor outside of the lunchroom to do theirs. Today however, the principal of my school was walking around and saw me typing on my iPad. He then proceeded to yell at me saying things like, you need to be where you're supposed to be! And NEVER pull something like this again! I'm a very good student, I look like the farthest thing from trouble. I want to talk to him and let him know why I was there, I dance 18 hours during the week, and I go to school 45. I'm severely depressed and am not interested in hanging out with other 13 year olds. Should I address my principal? I personally feel like adults don't listen to what kids have to say and just think they're all obnoxious, dumb, wastes of space. That last part might have been an exaggeration. :) thanks for all answers!

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