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Regular and Irregular Polygons

In this worksheet, students distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

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'Regular and Irregular Polygons' worksheet

Key stage:  KS 2

Year:  Year 3 11+ worksheets

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   2D Shapes: Triangles, Quadrilaterals and Polygons

Difficulty level:  

Worksheet Overview

In this worksheet, decide whether a polygon is regular or irregular.


The word polygon comes from the Greek language:

polús means many and gõnía means angles.


A polygon is a flat shape with straight sides that are joined to form a closed shape. It will have several angles.


Regular polygons

A regular polygon is one in which all the sides are equal in length and all the interior angles are equal in size.



A square has 4 equal sides and 4 equal angles of 90°.



A regular pentagon has 5 equal sides and 5 equal angles of 108°.



A regular octagon has 8 equal sides and 8 equal angles of 135°.



Irregular polygons

An irregular polygon is one in which either all the sides are not equal in length and/or all the interior angles are not equal in size.


 Scalene triangle

This triangle is scalene. It has sides of 3 different lengths and 3 different angles. It is irregular.


 Irregular pentagon

This pentagon has three 90° angles, but also two angles which are larger. The sides are of differing lengths. It is irregular.

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