When I brought it home and started looking through my stash for a suitable lining material, I discovered a very soft brown wool that I'd forgotten I had. Perfect! And just the right size, too.
I made a drawing of my pattern in MS Paint! Dig my crazy computer skillz, yo. As you can see (I hope) it's pretty simple: just cut on the angled line, and use the leftover wedge as a gore in the back.
Thanks to math, the cloak will hang down much farther in the back than it does in the front. It won't join up evenly at the back seams, but just shape it however you like with scissors and hem it up. What you end up with is basically a half-round cape with a nice hood. By changing the shape of the triangle at the top, you can make the hood as long or short as you want, or you could leave it square, or cut it into a liripipe.
Because mine is wool, and lined, I want to let it stretch a bit before I hem it up, so mine's hanging on my sewing mannequin Imogene for now. Look closely: you can see the pins.
My camera has a tendency to distort colors, and this tendency is really apparent here. The cloak looks much brighter than it actually is. I swear it's not orange! The blue is not that intense!
I still need to hem this, and devise some sort of fastener for the front. More as it gets there!