Question

what is the relationship between area and mass

Answer 1

Nothing, really.

Let's look at some dimensional analysis here:

Area has units of "length squared", such as square meters, square feet, or the like.

Mass has units of mass. It's a standard unit, the SI unit for it being kilograms. Note that mass is not the same as weight - weight is a measure of the force exerted by a certain mass when in the presence of a gravitational field, and on earth they are for all practical purposes proportional to one another.

So, at a cursory glance, they are completely independent of each other, however, consider density, with units of mass per unit volume.

Now, volume is not the same as area - area takes units of length squared, whereas volume is length cubed. They are related to each other by a dimension of length. And this volume is related to mass /only/ if density is considered.


Basically, mass and area have no intrinsic relationship with each other, unless we ascribe an arbitrary comparison of density as well as relating area to a certain volume.

Answer 2

Sometime, we consider materials like iron plate has area density. Area density usually called sigma. The relation is:
\[m=\sigma A\]