Question

write an application to the Principal of your school for apologizing for coming late to the school.

Answer 1

Just put the direct reason and that would do it.
 
Dear Professor,

Good day, I do apologize for coming late. The transport that I am expecting to arrive at the station was late for like an hour and that makes me unable to attend to your class. I will try to avoid this kind of incidents on the future and I will try to cope with the lessons I missed. Thanks for your understanding. Name.