The principal has cancelled the prom you are trying to persuade him or her using logos ethos and pathos

Ethos would be the answer

As you know, I am an upstanding member of the academic team, basketball team, volleyball team, student counsel, and future engineer club. Being an outstanding student and athlete, I hope that you will find my objection to your cancelling of my senior class prom compelling. My family and I have attended church with you and your son, who graduated last year, my entire life. I've always found you to be a reasonable and caring man, who always has his students' best interest at heart. Prom is a right of passage for every high school student. It is a night to celebrate the friendships, long years of gruesome school work, and the coming of our adult lives. We have worked extremely hard on the fundraisers to pay for prom. It would be a waste of all the time and effort put into it, if you cancel prom.

Ethos means to show the ethics of the situation or your good character.

Pathos - means to try to incline to their emotions.

Logos - means to appeal to their reasoning or logic.