I’m trying to create a button which looks something like this:
With each third acting as a separate button. I’m looking for advice on how to implement this. I’ve read a few posts about circular buttons, but this is a slightly different issue, as the buttons themselves are rather irregular shapes.
Thanks in advance.

I would create a Custom View, as @CommonsWare hinted at. That document covers everything, but basically you’ll render that image into a Canvas (fill the square, draw the circle, draw the three lines, then draw the text) and detect touch events yourself, doing a little math to figure out which segment was pressed. Android makes this surprisingly easy.