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Let $A$ be the initial plan area and take compression normal to the sheet. Smooth plates exert no lateral traction, so the uniaxial stress is ${\sigma }_z=-F/A$ and the two lateral strains are ${\epsilon }_x={\epsilon }_y=\nu F/(EA)$. To first order in strain,This area expansion under uniaxial compression is the increase of the sheet's plan area, equivalently the area of either broad face. Counting the sum of both broad faces would give twice this change; edge area would require thickness information. The cancellation of $A$ is a small-strain linear-elastic result, not a statement that arbitrarily large compressions need no geometry data.