There is no consistency in usage.
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Yes a square inch is larger than a square cm
Cell have a greater surface area to volume rations than a larger cell.
A soccer ball has a larger radius than a baseball, so it has more surface area.
Yes, the perimeter of a rectangle can be larger than its area. For example, consider a rectangle with dimensions 1 unit by 1 unit, which has a perimeter of 4 units and an area of 1 square unit. As the rectangle's dimensions change, especially when one dimension is much larger than the other, the perimeter can exceed the area even more significantly.
The answer will depend on what Region A and Region B are. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.