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Square units are used to measure the area of something.
yes
If you are talking about a rectangle, you can't find the area from just the perimeter. With a perimeter of say 80 units, the sides could be 10 and 30, with an area of 300 square units. But the sides could also be 5 and 35, with an area of 175 square units. There are lots of other possibilities. If you are talking about a square, that's different. Each side is a quarter of the perimeter, so the area is a quarter of the perimeter multiplied by a quarter of the perimeter.
Fahrenheit, if you're talking about U.S. Customary units.
Yes. But, it is seldom used.