Geometry › Polygons
Polygons
A polygon is any closed shape made of straight sides. The names go up by Greek prefixes — and the angles obey one neat formula.
Polygon explorer
Slide the side count and watch every angle update.
Interior angle sum
720°
(n−2) × 180
Each interior angle
120.0°
sum / n
Each exterior angle
60.0°
360 / n
Diagonals
9
n(n−3)/2
Naming polygons
- 3 sides — triangle
- 4 sides — quadrilateral
- 5 sides — pentagon
- 6 sides — hexagon
- 7 sides — heptagon
- 8 sides — octagon
- 10 sides — decagon
- 12 sides — dodecagon
- n sides — n-gon
Regular vs irregular
A regular polygon has every side the same length and every angle the same size. A regular triangle is equilateral. A regular quadrilateral is a square. Anything else is irregular.
Sum of interior angles
(n − 2) × 180°. So a pentagon's angles sum to 540°, a hexagon's to 720°.Convex vs concave
A convex polygon has every interior angle less than 180°. A concave (or non-convex) polygon has at least one reflex angle — it caves in.
Diagonals
A diagonal joins two non-adjacent vertices. For an n-gon there are n(n − 3) / 2 of them. A pentagon has 5, a hexagon has 9, a decagon has 35.