There are different formulae for different shapes.
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Area = ( length of a side)2
Yes, LxW=Area. For Surface Area, add up the area of all the sides
surface area=(perimeter of base)x(height of the shape)+(area of the base)x(2)
Calculus can be used to find the surface area of any object given that you know the equation describing said object. It's usually easier to find the area from experiment or through using a combination of existing models to approximate the surface area
It is area