Formula and example
How it is calculated
A = n·s²/[4·tan(π/n)], P = n·s. Inradius = s/[2·tan(π/n)], circumradius = s/[2·sin(π/n)].
Worked example
A regular hexagon with 2 cm sides has a perimeter of 12 cm, an area of 6√3 ≈ 10.3923 cm² and 9 diagonals.
Things to check
- All sides and all interior angles must be equal. A general irregular polygon needs more information.
- The number of sides must be an integer of at least 3.
Frequently asked questions
How are the diagonals counted?
Each vertex connects to n−3 non-adjacent vertices. Each diagonal is counted twice, so the total is n(n−3)/2.