'What is a piano classified as?

It depends actually. There are 3 possibilities here.

1) percussion because the hammers in a piano hit the strings to make the music

2) strings because the hammers hit the strings so it's not the hammers making the music but the strings

3) keyboard because now not all people can agree on percussion or strings so they gave it its own category. Also they have keyboards which don't have strings or hammers

Personally though, I like calling it a percussing or a strussion. :)