Area is usually not measured, but calculated. For several standard shapes (for example, rectangles, circles, etc.) there are standard formulae to calculate the area; for an arbitrary irregular shape, integration can be used. This basically means mentally cutting the shape into lots of small pieces.
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Area is measured in terms of square units covered. In a few cases there may be formulae which allow you to calculate the area, or by integration. In many cases it has to be estimated using a grid.
Length squared
NO! It's measured in cm2
Area is not measured in units cubed so this question makes no sense.
None. Area cannot be measured in length units - only in squares of such units.
Because the perimeter is a linear measurement, and area is measured by multiplying 2 linear measurements together.