Classifying two-dimensional shapes

Regular polygons

An important way in which we can categorize polygons is by recognizing those that are regular and those that are not. A regular polygon is one in which all the sides are the same length and all the angles are the same size.

For example, a regular octagon has eight equal sides and eight angles, each of which is equal to 135 degrees. To work out the angles in a regular polygon, use the rule (2n-4 right angles) to determine the total of the angles in the polygon (thus, for an octagon the sum is 2 x 8 – 4 = 12 right angles, that is, 1080 degrees divided by 8 = 135 degrees).

Give pupils opportunity to explore the properties of various shapes, including the different kinds of triangles and quadrilaterals, and regular and irregular shapes, by folding, tracing, matching, looking for reflective and rotational symmetries, and drawing out the implications of these.

The word ‘regular’ is often misused when people talk about shapes, as though it were synonymous with ‘symmetric’ or even ‘geometric’. For example, the rectangular shape of the cover of a book is not a regular shape, because two of the sides are longer than the other two - unless you happen to have picked an unusual book that is square in shape.

It is disappointing when every time you see an example of, say, a pentagon (or a hexagon) used in material for primary pupils it seems to be a regular one. This confuses the distinction between a pentagon in general and a regular pentagon.