Regular and Irregular Polygons

Polygons

A polygon is any 2-dimensional (2D) shape which is made up of straight lines. Triangles, quadrilaterals and octagons are all types of polygon, each with a different number of sides. A circle is not a polygon because it does not have straight edges.

A polygon can be regular or irregular.

A regular polygon has all sides of equal length, and all angles of equal size.

An irregular polygon has sides of different lengths and angles of different sizes.

Examples

• A square is a regular polygon as all of its 4 sides are equal in length and all of its 4 angles are the same size, 90°.
• A rectangle is an irregular polygon because it does not have 4 sides of equal length, though it does have equally sized angles.
• A rhombus is an irregular polygon because although it does have 4 sides of equal length, it does not have equally sized angles.

Polygons: square, rectangle and rhombus

Labelling features of polygons

When drawing a polygon, dashes or hatch marks are used to indicate congruent sides. Congruent means the sides are of equal length. Sides with different numbers of hatch marks on them are not the same length.

Arcs and double arcs, like in the image of the rhombus above, can be used to indicate angles which are the same size.

• The square in the image above shows 4 sides with single hatch marks, meaning those sides are all equal in length.
• The rectangle shows 2 sides (top and bottom) with a single hatch mark, meaning those sides are equal in length. It also has 2 sides (left and right) with double hatch marks, indicating that those sides are also equal in length.
• The rhombus shows 2 angles (top and bottom) indicated by a single arc, meaning those angles are both equal in size. It also has 2 angles (left and right) indicated by double arcs, so again meaning that those angles are equal in size.

Naming polygons

Polygons have different names depending on their properties. The number of sides that a polygon has is represented by its name.

Look at the different names in the table opposite that are used for different types of polygons, according to how many sides they each have.

Other particular words are also used to describe common shapes – for example, a ‘regular triangle’, which has 3 equal sides, is usually referred to as an equilateral triangle. Don’t confuse this with the other types of triangle – an isosceles triangle that has two equal sides and a scalene triangle that has no equal sides.

A ‘regular quadrilateral’ is normally just called a square.

Regular or irregular?

Other regular polygons have the prefix ‘regular’ followed by their name, eg regular hexagon.

If a polygon is irregular, you use the term in a similar way, eg irregular pentagon.

Regular hexagon and irregular pentagon