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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?
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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.
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Last note: the info about the area is not relevant to the problem.
It doesn't carry (doesn't bring) new information.