Know that a regular polygon has sides that are the same length and angles that are the same size | Maths

Starter quiz

Match the shape to the correct name.

a

⇔

hexagon ✓

b

⇔

square ✓

c

⇔

pentagon ✓
Which of these shapes has right angles?

equiliateral triangle

square ✓

regular pentagon
Which of these shapes are squares?

A

B ✓

C ✓

D
Which of these are straight lines?

A ✓

B ✓

C
Select all the shapes that have only straight sides.

A

B ✓

C

D ✓
Select all the two-dimensional (2D) shapes.

A

B ✓

C

D ✓

Exit quiz

Select all of the statements that are true of polygons.

They are three-dimensional shapes.

They have all straight sides. ✓

They have all closed sides. ✓

All interior angles are right angles.
Which of these shapes is a regular polygon?

A ✓

B

C

D
Which of these shapes are regular polygons?

A

B

C ✓

D ✓
This shape has been made by putting number rods together. Select all of the statements that are true.

The sides are equal in length. ✓

The sides are different lengths.

The interior angles are equal.

The interior angles are unequal. ✓

It is a regular polygon.
These shapes have been made by putting number rods together. Look closely at the sides shown by the lines. Which one is a regular polygon?

A

B

C ✓
Select all of the statements that are true of regular polygons.

They are two-dimensional, closed shapes. ✓

They are two-dimensional, open shapes.

They have all straight sides. ✓

No sides are equal in length

All interior angles are equal. ✓

Worksheet

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Lesson Details

Key learning points

In a regular polygon, the sides are all the same length and the angles are all the same size
In an irregular polygon the sides and angles are not all the same sizes
Irregular polygons can have some angles and sides the same sizes

Common misconception

Many polygons appear regular as all of the sides are the same length. However, it is possible (as the lesson shows) to have polygons which are the same length sides but different interior angles.

Pupils should have previous experience of right angles. Use a right angle 'measurer' to prove that some of the angles in a shape are greater than a right angle and some smaller; as the angles are not all equal, it is not a regular polygon.

Keywords

Regular polygon - A polygon where all angles are equal and all side lengths are equal.
Irregular polygon - A polygon where not all angles are equal and / or not all side lengths are equal.
Interior angles - Interior angles are the angles formed inside a polygon by two of its sides.