A centimetre is a unit of length. A square centimetre is a unit of area. The two units are therefore incompatible.
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Area = 16*24 = 384 square cm
Yes, it can exist.
Oddly enough the perimeter is 16 centimeters.
A perimeter is a measure of length and so cannot be 16 square centimetres - which is a measure of area. As it happens, a square with a perimeter of 16 centimetres will have sides of 4 cm and so an area of 16 square centimetres.
3 cm