Area of a regular polygon calculator
Enter the dimensions of a regular polygon and read off its area, its perimeter and the quantities that follow from them.
Area
41.569 219m²
- Perimeter
- 24
- Apothem (inradius)
- 3.464 101 6
- Circumradius
- 4
- Interior angle
- 120.0000 degrees
- Number of diagonals
- 9
Show the working
- Number of sides = 6
- Side length = 4
- Area = 6 * 4^2 / (4 * tan(pi/6)) = 41.5692
- Perimeter = 6 * 4 = 24
- Apothem (inradius) = 4 / (2 * tan(pi/6)) = 3.4641
- Circumradius = 4 / (2 * sin(pi/6)) = 4
- Interior angle = (6 - 2) * 180 / 6 = 120
- Number of diagonals = 6 * (6 - 3) / 2 = 9
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- area = n s^2 / (4 tan(pi/n))
- apothem = s / (2 tan(pi/n))
- interior angle = (n - 2) x 180 / n
- diagonals = n(n-3)/2
Lengths are entered in metres by default; switch any field to feet, inches or millimetres and the conversion is exact.