Find the number of sides for a regular polygon if the area is 480, the side length is 10 and the apothem is 6.
Find the number of sides for a regular polygon if the area is 480, the side length is 10 and the apothem is 6.
@Mathematics

Question

Find the number of sides for a regular polygon if the area is 480, the side length is 10 and the apothem is 6.
 Find the number of sides for a regular polygon if the area is 480, the side length is 10 and the apothem is 6.
 @Mathematics

anonymous · Answer

The area can be computed using only the number of sides and the side length.

A regular polygon with 8 sides of length 10 has an area of$$200 \text{ Cot}\left[\frac{\pi }{8}\right] $$or 482.8 to the nearest tenth of a square unit.

The area for a polygon of 7 sides and 9 sides, side length of 10, is 363.4 and 618.2 square units respectively.