With the rigid stuff, if you worked out how to cut it so the full sheet made you however made equilateral triangles you can get out of it, without any waste and then cut a few up in the same manner you could just stack them on top of each other in the corner perhaps. or even buy/make (plywood would work great) a shelf that matched that shape that you could stack say 10/15 of the triangles on and then put another plywood triangle on top you could then staple some material to the plywood to stop the fibres from escaping and make it look nicer.
As for material. I just went with cotton from 'Boyes' i don't know if you have one of these shops near you but you can order sheets of cotton, calico, muslin for a little over a pound a meter online. That does the job nicely!