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The units used for area are squared length units, where the length units are: meter, inch, feet, etc.
The units used for surface areas are length units (meters, inches, feet, etc) squared.
Why we use those? Because area is defined as the product between the two dimensions (two sides of rectangle, for example) of a figure. And these dimensions are given in length units. So if we take the product of two of these, we will get squared length units.
The difference with volume units, is that for volume we need 3 dimensions, then we will have cubed length units.
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