Geometry
Polygons
Perimeters, angles and diagonals of regular polygons.
Geometry
Regular polygon perimeter
P = n × a→GeometryRegular polygon interior angle
α = (n − 2) × 180° / n→GeometryNumber of polygon diagonals
D = n(n − 3) / 2→GeometryRegular polygon apothem
aₚ = a/(2 tan(π/n))→GeometryRegular polygon circumradius
R = a/(2 sin(π/n))→GeometryRegular polygon area from apothem
S = naaₚ/2→GeometryPolygon area from perimeter and apothem
S = Paₚ/2→GeometryRegular polygon central angle
φ = 360°/n→GeometryRegular polygon exterior angle
β = 360°/n→GeometrySide from radius and central angle
a = 2R sin(φ/2)→GeometryApothem from radius and side
aₚ = √(R²−(a/2)²)→GeometryPolygon interior angle sum
Σ = (n−2)·180°→GeometryPolygon exterior angle sum
Σext = 360°→