  # Regular and Irregular Polygons

In this worksheet, students distinguish between regular and irregular polygons based on reasoning about equal sides and angles. Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

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

Difficulty level:   ### QUESTION 1 of 10

In this worksheet, you must 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. This triangle is scalene. It has sides of 3 different lengths and 3 different angles. It is irregular. This pentagon has three 90° angles, but also two angles which are larger. The sides are of differing lengths. It is irregular.

---- OR ---- 