Geometry Intermediate

Regular Polygon Properties

Choose any regular polygon from triangle to dodecagon. Enter a side length or circumradius and instantly get area, perimeter, apothem, and interior angles — with full step-by-step work.

3–12 sides
Side length or circumradius
Live polygon diagram
Input
Try:
Result
Select sides and enter a value.
Step-by-Step Solution
Polygon Diagram
Key Formulas (n sides, side s)
Circumradius R = s / (2 sin(π/n)) Apothem a = s / (2 tan(π/n)) Area = ½ · a · P where P = n·s Interior angle = (n−2)·180° / n
Given Circumradius R

If R is given instead: s = 2R·sin(π/n), then apply the same formulas for apothem and area.

The circumradius is the distance from center to vertex; the apothem is center to midpoint of a side.

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