Equally extrude these vertices inside the shape I'd like to extrude these faces toward the center of the shape equally - say a 5cm. Try as I might, I can't figure it out. Lots of solutions show inset for faces, but this is just a shape of vertices. There must be a way. I'm in 2.8
The way I do this is by selecting all the vertices and making a NGon by pressing F. Then 
I use inset and delete the innermost face.