Because it's plastic I wouldn't get a soldering iron near it. That could cause toxic off-gassing. If it was something I really liked I'd probably bury the broken end in one of the garden beds and use it for a backdrop to flowers. That's what I've done with several pottery plates that I couldn't bear to part with.
Sad to say, I would not try to fix it. I see many glass versions of this at thrift shops each time I go and I would buy one of those, unless you feel the glass too heavy.