SOLUTION: A certain regular polygon has a perimeter of 80 cm; its apothem is 12.1 cm. The polygon’s area is 484 cm². How many sides does the polygon have?

The equation to determine n, the number of sides of the polygon, is


 = ,   or

 = .   (*)

I tried to guess n to get the equality, using Excel.

It looks like n = 8 is the solution. It gives closest approximation, but still not exact solution.

Then I checked the apothem value for 8-gon with the side length 10 cm, which gives the perimeter 80 cm.

Its apothem is 12.071 cm instead of 12.1 cm.

With this data the solution n = 8 of (*) is very convincing.