Different polygons have different relationships between perimeter and area. For example, if we assume regular polygons, an equilateral triangle and a square have different perimeters for the same area. If you allow irregular polygons, the variety is even bigger.
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Only if you know what kind of polygon you have. If you know that you have a hexagon and one side is 1 cm, the perimeter is 6 cm. You only have to know the length of one side, since a regular polygon has equal sides. Perimeter or a regular polygon is the length of each side times the number of sides. You need to know both pieces to find the perimeter. ■
There can be no such formula in general. A formula will exist if the area is a regular polygon (or a circle).
In general you cannot find the perimeter of any shape if only the area is given.
There is no perimeter of a circle. Only flat shapes have perimeters. You can however, find the circumference, surface area, and volume.