How to find the area of a regular polygon with only the apothem?

Find the length of the sides plus the the apothem. Solution: Plug in what you know into both the area and the perimeter formulas to solve for the length of a side and the apothem.

Hopefully this sounds smart ... If the drawing of your octagon (or whatever) has been separated into triangles, and one triangle's area is labeled, then you do not need to know the apothem. Just take the area of that one triangle, and multiply by the number of sides in the original polygon.