Piece from bottom of Prius

It most definitely looks like part of an exhaust shield. Muffler shop will tell the story.
You ever been to Sembach?

Oop's, I see that you're to young to answer that ?

 

As Bzzap! said, it's a heat shield around the exhaust. I've had these fall off of at least one other car I've owned; they get hot, they're exposed metal, and Corrosion R Us. There's usually some pretty entertaining sounds in the (usually short) time before they fall off; when the noise stopped on this old minivan I owned I pulled, over, walked back 50 yards, and picked it up off the road.

The dangers, such as they are, of running without the heat shield usually involve setting dry leaves afire if they happen to be under the car when one parks. Not to mention hot spots that might melt the sound absorbing/corrosion preventing material on the car.

I'd guess that reattaching same involves a little spot welding; but that's what muffler shops know how to do.

Good luck!