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you can save the hinge and reuse it, iv done that on a few glass tops. mite even be able to cut the handel off and put it on the new glass with some 3m two sided foam tape(find at walmart of a hardware store, or even autozone) its used to hold the badges on your car, like the f-series or the 1500 badges on pickup truck fenders
You also don't want to use plexiglass. If you use a thin piece, the heat from your light will warp it. If you go too thick, your light will be worthless.
Go to a glass store and get a piece cut is a good idea but probably not the cheapest.
Or, got to a LFS and get a new one. I have many spare parts from replacing glass canopies, never know when you'll need a new hinge since they do wear out.