What Is a Polygon? Names, Sides and Angles

Polygon

A closed two-dimensional shape made only of straight sides, each side meeting two others end to end.

Où les élèves le rencontrent: Grade 3 or 4 mathematics, when flat shapes are named, and again at GCSE for interior and exterior angle rules.

La réponse en bref
A polygon is a closed, flat shape whose sides are all straight lines — a triangle, a pentagon and a hexagon are all polygons. It is regular only when every side and every angle is equal. A circle is not a polygon, because it has no straight sides at all.

Un exemple

Interior angles of an n-sided polygon = (n − 2) × 180°

A hexagon has 6 sides, so its angles add to (6 − 2) × 180° = 720°. If it is a regular hexagon, each angle is 720° ÷ 6 = 120°. The rule works because any polygon can be cut into triangles from one corner, and an n-sided polygon always gives n − 2 of them.

The names from three sides to twelve

Polygons are named by their number of sides, using Greek number words. The ones worth knowing by heart stop at twelve; beyond that, mathematicians simply say a 15-sided polygon or a 15-gon.

A few have alternative names in circulation. The heptagon is occasionally called a septagon, which mixes Latin and Greek and is best avoided, and the nonagon is sometimes called an enneagon.

3 sides — triangle
4 sides — quadrilateral
5 sides — pentagon
6 sides — hexagon
7 sides — heptagon
8 sides — octagon
9 sides — nonagon
10 sides — decagon
11 sides — hendecagon
12 sides — dodecagon

Regular means two things at once

A regular polygon has all its sides equal and all its angles equal. Both conditions are needed, and shapes that satisfy only one are common enough to catch people out.

A rhombus has four equal sides but its angles are not all the same, so it is not regular. A rectangle has four equal angles but two different side lengths, so it is not regular either. A square meets both conditions, which is exactly what makes it the regular quadrilateral.

Everything else is irregular, and that is not a criticism — most polygons in the world are irregular. It only means the interior angles have to be worked out individually rather than divided out equally.

Why a circle is not a polygon

Because a polygon is made of straight sides and a circle has none. Increasing the number of sides makes a polygon look more and more circular — a hundred-sided polygon is hard to tell from a circle by eye — but it still has a hundred corners and a hundred straight edges, and a circle has neither.

The same rule rules out a semicircle, which has one straight edge and one curved one, and any shape that does not close up. A polygon must return to where it started, with every side meeting exactly two others.

Questions fréquentes

Is a square a polygon?

Yes — a square is a polygon with four straight sides, which makes it a quadrilateral, and since all four sides and all four angles are equal it is the regular quadrilateral. Rectangles, rhombuses, kites and trapeziums are all quadrilaterals too, but none of them is regular.

What do the interior angles of a polygon add up to?

(n − 2) × 180°, where n is the number of sides: 360° for a quadrilateral, 540° for a pentagon, 720° for a hexagon. The exterior angles behave more simply — they always add to 360° for any polygon, which is why each exterior angle of a regular one is 360° ÷ n.

What is a concave polygon?

One with a dent in it, meaning at least one interior angle is bigger than 180° — a reflex angle. An arrowhead is the standard example. Polygons with no such angle are called convex, and every regular polygon is convex.

Is a cube a polygon?

No. A polygon is flat, and a cube is a solid, so it belongs to a different family called polyhedra. The connection is that each of a cube's six faces is a polygon — a square, in fact — and most solids studied at school have polygons for faces.

Dernière mise à jour 21 août 2026

Polygons: Straight Sides, Closed Shape