You can also do it without adding extra styles just using the Angular Material elements.
Basically you need to add layout to all the parents of the elements you want to fill vertically. You also don’t need to use so many layout-fills.
Here the demo: http://plnkr.co/edit/E244WNhvMXw9VC7DpAW0?p=preview
I also added a background color to the sidebar to demonstrate that it also fills vertically.