Polygons

Properties of Regular Polygons

Polygon

A polygon is a plane shape (two-dimensional) with straight sides. Examples include triangles, quadrilaterals, pentagons, hexagons and so on.

Regular

A "Regular Polygon" has: all sides equal and all angles equal. Otherwise it is irregular.

Regular Pentagon   Irregular Pentagon

Here we will be looking at Regular Polygons only.

Properties

So what can we know about regular polygons? First of all, we can work out angles.

Exterior Angle The Exterior Angle is the angle between any side of a shape, and a line extended from the next side.

All the Exterior Angles of a polygon add up to 360°, so: Each exterior angle must be 360°/n (where n is the number of sides) Press play button to see.

Example: What is the exterior angle of a regular octagon?

An octagon has 8 sides, so:

Exterior angle = 360°/n = 360°/8 = 45°