Maths
What is a polygon?
Quick answer
A polygon is a flat shape made only of straight sides that close up completely. Triangles, squares, pentagons and hexagons are polygons; a circle is not.
In one sentence
A polygon is a closed, flat shape with straight sides, named after the number of sides it has.
Explained
The word polygon comes from Greek words meaning "many angles". To be a polygon, a shape must be flat, closed (no gaps) and made of straight sides. A circle fails because its edge is curved. A shape with a gap in it fails because it is open.
ruler
pencil
blocks
| Sides | Name |
|---|---|
| 3 | triangle |
| 4 | quadrilateral |
| 5 | pentagon |
| 6 | hexagon |
| 7 | heptagon |
| 8 | octagon |
| 9 | nonagon |
| 10 | decagon |
| 12 | dodecagon |
Polygons can be regular or irregular. In a regular polygon, all sides and all angles are equal: a square, an equilateral triangle, a stop sign. The stop sign is a regular octagon. In an irregular polygon, the sides or angles differ, like most rectangles (equal angles but unequal sides).
Polygons can also be convex, where every corner points outwards, or concave, where at least one corner points inwards, like an arrowhead. See also 2D shapes, quadrilaterals and types of triangles.
For older children, there is a neat pattern. A polygon with n sides can be cut into (n − 2) triangles, so the angles inside it add up to (n − 2) × 180 degrees. A triangle has 180, a quadrilateral 360 and a pentagon 540. In a regular hexagon, the six angles add up to 720 degrees, so each is 120 degrees. That is why hexagons fit together without gaps, like the cells of a honeycomb.
Examples
| Polygon | Where you see it | Angles add up to |
|---|---|---|
| Triangle | road sign, roof | 180° |
| Quadrilateral | window, book | 360° |
| Pentagon | the Pentagon building in the USA | 540° |
| Hexagon | honeycomb, nuts and bolts | 720° |
| Octagon | stop sign | 1,080° |
Common mistakes
- Counting corners wrongly. The number of corners equals the number of sides.
- "A regular shape means a normal shape." Regular means all sides and all angles are equal.
- Including shapes with curves. Semicircles and ovals are not polygons.
Quick quiz
Polygons
Check what you know with 4 quick questions.
Question 1 of 4
Which of these is not a polygon?
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For grown-ups
Related topics
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
Angles
An angle measures the amount of turn between two lines that meet at a point. Angles are measured in degrees (°); a right angle is 90° and a full turn is 360°.
Quadrilaterals
A quadrilateral is any flat shape with four straight sides. Squares, rectangles, rhombuses, parallelograms, trapezia and kites are all quadrilaterals, and their angles add up to 360 degrees.
Types of triangles
Triangles are named by their sides (equilateral, isosceles, scalene) or by their angles (acute, right-angled, obtuse). The three angles of any triangle add up to 180 degrees.
Area
Area is the amount of flat space inside a shape, measured in square units like cm² or m². A rectangle 4 cm by 3 cm has an area of 4 × 3 = 12 cm².
Parts of a circle
A circle has a centre, a radius, a diameter and a circumference. The radius runs from the centre to the edge, and the diameter is twice the radius.