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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.

'Regular and Irregular Polygons' worksheet

Key stage:  KS 2

Curriculum topic:  Geometry: Properties of Shapes

Curriculum subtopic:  Understand Polygons

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

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.

 

  Square  

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

 

Pentagon

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

 

 Octagon

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.

Is the following polygon regular or irregular?

 

Equilateral triangle

An equilateral triangle

regular

irregular

Is the following polygon regular or irregular?

 

Isosceles triangle

An isosceles triangle

regular

irregular

Is the following polygon regular or irregular?

 

Right-angled triangle

A right-angled triangle

regular

irregular

Is the following polygon regular or irregular?

 

Hexagon

regular

irregular

Is the following polygon regular or irregular?

 

Hexagon

regular

irregular

Is the following polygon regular or irregular?

 

Rhombus

A rhombus

regular

irregular

Is the following polygon regular or irregular?

 

Rectangle

A rectangle

regular

irregular

Is the following polygon regular or irregular?

 

Decagon

regular

irregular

Is the following polygon regular or irregular?

 

Trapezium

A trapezium

regular

irregular

Is the following polygon regular or irregular?

 

Rotated square

A rotated square

regular

irregular

  • Question 1

Is the following polygon regular or irregular?

 

Equilateral triangle

An equilateral triangle

CORRECT ANSWER
regular
EDDIE SAYS
An equilateral triangle has all 3 sides and all 3 angles equal.
  • Question 2

Is the following polygon regular or irregular?

 

Isosceles triangle

An isosceles triangle

CORRECT ANSWER
irregular
EDDIE SAYS
An isosceles triangle only has 2 sides equal and 2 angles equal.
  • Question 3

Is the following polygon regular or irregular?

 

Right-angled triangle

A right-angled triangle

CORRECT ANSWER
irregular
EDDIE SAYS
A right-angled triangle has one angle of 90° and two other smaller angles.
  • Question 4

Is the following polygon regular or irregular?

 

Hexagon

CORRECT ANSWER
regular
EDDIE SAYS
This is a regular hexagon.
  • Question 5

Is the following polygon regular or irregular?

 

Hexagon

CORRECT ANSWER
irregular
EDDIE SAYS
This is an irregular hexagon.
  • Question 6

Is the following polygon regular or irregular?

 

Rhombus

A rhombus

CORRECT ANSWER
irregular
EDDIE SAYS
A rhombus has 4 equal sides, but the angles are not all the same.
  • Question 7

Is the following polygon regular or irregular?

 

Rectangle

A rectangle

CORRECT ANSWER
irregular
EDDIE SAYS
A rectangle has 4 equal angles, but the sides are not all the same.
  • Question 8

Is the following polygon regular or irregular?

 

Decagon

CORRECT ANSWER
regular
EDDIE SAYS
This is a regular decagon.
  • Question 9

Is the following polygon regular or irregular?

 

Trapezium

A trapezium

CORRECT ANSWER
irregular
EDDIE SAYS
A trapezium does not have 4 equal sides.
  • Question 10

Is the following polygon regular or irregular?

 

Rotated square

A rotated square

CORRECT ANSWER
regular
EDDIE SAYS
A square is regular whether it is rotated or not.
---- OR ----

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