Understand Regular and Irregular Polygons Worksheet

A polygon is a flat, 2D shape.

It has straight sides and is fully closed.

All of the sides are straight and joined up.

Polygons can have any number of sides.

Regular polygons:

A regular polygon has all sides of the same length and all sides at the same angle.

An equilateral triangle is a regular polygon; all of its sides and angles are the same.

Irregular polygons:

An irregular polygon is a shape with sides and/or angles at differing lengths and sizes.

A scalene triangle has differing angles and sides.

Look at the shapes shown below.

Choose which shape is an irregular polygon.

Rectangle Decagon

rectangle Decagon

Rotated Square Equilateral triangle

Rotated square Equilateral triangle

Look at the shapes shown below.

Can you correctly match the statements about the shapes?

Right Arrow Decagon

Decagon

Rotated Square Equilateral triangle

Rotated square Equilateral triangle

Column A	Column B
Equilateral triangle	This shape can also be called a quadrilateral
Rotated square	This regular polygon has 10 sides
Decagon	All of the sides and angles are equal
Right arrow	This shape is irregular and the odd one out

Laura states that the semicircle below is a regular polygon.

Is she correct or incorrect?

Semicircle

Correct

Incorrect

Is this shape a polygon?

Type yes or no.

Shape with intersecting lines

Is this shape a polygon?

Type yes or no.

Shape with gap

Read each statement carefully about polygons and choose which are correct.

Look at the polygons below and write the name of the regular polygon.

Square Scalene triangle Pentagon Rhombus

Look at the shapes below and write the name of the irregular polygon.

Rotated square Trapezium Equilateral triangle Hexagon

Lydia stated,

"A square is a rectangle."

Is Lydia correct or incorrect?

Incorrect

Correct

Harry states,

"A rhombus is a parallelogram."

Is Harry correct or incorrect?

Incorrect

Correct

ANSWERS

Question 1

Look at the shapes shown below.

Choose which shape is an irregular polygon.

Rectangle Decagon

rectangle Decagon

Rotated Square Equilateral triangle

Rotated square Equilateral triangle

CORRECT ANSWER

EDDIE SAYS

The rectangle is the irregular polygon as it has 4 equal angles but the sides are of differing lengths. How did you find this question? Don't worry we have more to for you to practise so that you get really confident!

ANSWERS

Question 2

Look at the shapes shown below.

Can you correctly match the statements about the shapes?

Right Arrow Decagon

Decagon

Rotated Square Equilateral triangle

Rotated square Equilateral triangle

CORRECT ANSWER

Column A	Column B
Equilateral triangle	All of the sides and angles are e...
Rotated square	This shape can also be called a q...
Decagon	This regular polygon has 10 sides
Right arrow	This shape is irregular and the o...

EDDIE SAYS

How did you get on matching the statements correctly? The equilateral triangle, rotated square and decagon are all regular polygons with equal sides and angles. The right arrow is irregular, as it doesn't have equal sides or angles that join the sides.

ANSWERS

Question 3

Laura states that the semicircle below is a regular polygon.

Is she correct or incorrect?

Semicircle

CORRECT ANSWER

Incorrect

EDDIE SAYS

Laura is incorrect, a shape with curved sides is not a polygon. A polygon must have straight sides only.

ANSWERS

Question 4

Is this shape a polygon?

Type yes or no.

Shape with intersecting lines

CORRECT ANSWER

No

EDDIE SAYS

No, this shape is not a polygon as it has sides that intersect. A polygon cannot have intersecting sides. You've got this, keep going.

ANSWERS

Question 5

Is this shape a polygon?

Type yes or no.

Shape with gap

CORRECT ANSWER

No

EDDIE SAYS

No, this shape is not a polygon as it has sides that are open. A polygon cannot have any gaps in its sides.

ANSWERS

Question 6

Read each statement carefully about polygons and choose which are correct.

EDDIE SAYS

How did you get on identifying the properties of 2D shapes? The correct statements are: Is a 2D shape. Has straight sides. Is a closed shape (no gaps). Are you finding this easier as you move through the questions?

ANSWERS

Question 7

Look at the polygons below and write the name of the regular polygon.

Square Scalene triangle Pentagon Rhombus

CORRECT ANSWER

Square

EDDIE SAYS

The only regular polygon shown is the square. The scalene triangle, pentagon and rhombus are all irregular polygons.

ANSWERS

Question 8

Look at the shapes below and write the name of the irregular polygon.

Rotated square Trapezium Equilateral triangle Hexagon

CORRECT ANSWER

Trapezium

EDDIE SAYS

The irregular polygon is the trapezium. The regular polygons are The rotated square Equilateral triangle Hexagon This question was a little more challenging so don't worry if you got it wrong!

ANSWERS

Question 9

Lydia stated,

"A square is a rectangle."

Is Lydia correct or incorrect?

CORRECT ANSWER

Correct

EDDIE SAYS

Yes, Lydia is correct. A square is a special type of rectangle. It is a special type of rectangle that has all sides the same length.

ANSWERS

Question 10

Harry states,

"A rhombus is a parallelogram."

Is Harry correct or incorrect?

CORRECT ANSWER

Correct

EDDIE SAYS

Harry is correct, a rhombus is a parallelogram. A rhombus is a parallelogram because opposite sides are parallel and opposite angles are equal (the same as a parallelogram).