Area of a regular pentagon calculator
Enter the dimensions of a regular pentagon and read off its area, its perimeter and the quantities that follow from them.
Area
27.527 638m²
- Perimeter
- 20
- Apothem
- 2.752 763 8
- Diagonal
- 6.472 136
Show the working
- Side = 4
- Area = 4^2 * sqrt(25 + 10*sqrt(5)) / 4 = 27.5276
- Perimeter = 5 * 4 = 20
- Apothem = 4 / (2 * tan(pi/5)) = 2.752 76
- Diagonal = 4 * phi = 6.472 14
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 = s^2 sqrt(25 + 10 sqrt 5) / 4
- the diagonal is the side times the golden ratio
Lengths are entered in metres by default; switch any field to feet, inches or millimetres and the conversion is exact.