If you open up the parasol and mark on the outside the struts, so you know the width of them, you could then take it and cut sections from middle of one strut to the middle of the next. This would give you a pattern piece, adding on 1.5cm for seam allowance on all side..
If this is still too long for fabric, you could cut pattern piece in half (adding seam allowances on new cut edges. ( I would transfer pattern onto paper first, I use baking paper for this, but you could use newspaper and feel where edges are).
By making pieces smaller, remember to add seam allowance.
If not leaving outside at night, you could use any fabric, or even patchwork it. Wash any fabric first