How do you work out how many sides a regular polygon has?

Answer 1

It depends upon what you know about the polygon:

• The name

Polygons are normally named based on Greek numbers:

Penta - 5

Hexa - 6

Hepta - 7

Octa - 8

Nona - 9

Deca - 10

Hendeca - 11

Dodeca - 12

The Hendecagon is sometimes referred to as a Undecagon.

Triangles are 3 sided and quadrilaterals are 4 sided.

• The exterior angle

The sum of the exterior angles of a polygon sum to 360o. With a regular polygon, these are all the same, so divide 360o by the exterior angle and it will give you the number of sides.

• The interior angle

First find the exterior angle of the polygon: since the exterior and interior angles of a polygon are supplementary, they sum to 180o, so subtract the interior angle from 180o to get the exterior angle; then use the method of the exterior angle above.