None! They both mean the same thing. For example, if your floor measures 3 meters long and 2 meters wide you would need 6 square meters of carpet. Alternatively you could say "My floor measures 6 meters squared." Five meters squared. This refers to a linear measure, five meters. It also tells what function to apply to the measure-- make a square with it. If I make a square with a five meter chain, I will end up with 25 square meters. Five square meters. This will be equivalent to five of the 25 squares that the above area contains. Quite different. If you have a floor measuring 3 meters by 2 meters and you ask the carpet guy for carpeting to cover 6 meters squared, you will get an unpleasant surprise.
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About 1.3 square meters. (1.30064256 square meters).
1 square centimeter = 0.0001 square meters
They mean the same thing. Square meters is the same as meters squared.
square meters or meters squared: m2
2.56 square meters