Polygons

Know what a polygon is, name polygons from triangle to decagon by counting their sides, and tell regular from irregular shapes.

In the exam for Edexcel IGCSE Maths 4MA1, Cambridge IGCSE Maths 0580, Cambridge O Level Maths 4024 · 24 real past-paper questions below

اقرأ هذا الدرس مشروحاً بالعربي ←

What Is a Polygon?

A polygon is a flat, closed shape made only of straight sides. A circle is not a polygon: it has no straight sides.

Word	Meaning
Side	one straight edge
Vertex	a corner (plural: vertices)
Regular	all sides equal and all angles equal
Irregular	not all sides or angles equal

Key idea

A square is a regular quadrilateral. A rectangle is irregular: its sides are not all equal.

Key idea

Polly the parrot flew out of the window. Where is she now? Polly-gone! In fact, polygon really does come from Greek: poly means 'many' and gon means 'angle' or 'corner'.

Names by Number of Sides

The 1-mark question: write down the mathematical name of a shape. Count the sides, then use the name.

Sides	Name
3	triangle
4	quadrilateral
5	pentagon
6	hexagon
7	heptagon
8	octagon
9	nonagon
10	decagon

Memory trick

An octopus has 8 legs: an octagon has 8 sides. A decade is 10 years: a decagon has 10 sides.

Common mistake

Mixing up hexagon (6) and heptagon (7). Hexagon has an x, like six.

Irregular Shapes Keep the Name

The name depends only on the number of sides. A shape with 6 sides is a hexagon, even if it is squashed or has a corner pointing in.

Steps

1
Put a tick on one corner.
2
Go round the shape, counting each side once.
3
Stop when you are back at the tick.

Common mistake

Only calling the neat, regular shape a hexagon. An irregular shape with 6 sides is also a hexagon.

Four-Sided Shapes Have Their Own Names

The 1-mark question can ask for the name of a quadrilateral. Look for parallel sides and equal sides.

You see	Name
Exactly one pair of parallel sides	trapezium
Two pairs of equal sides next to each other	kite
All four sides equal (often leaning over)	rhombus
Two pairs of parallel sides	parallelogram

Key idea

All of these are quadrilaterals. "Quadrilateral" is right but gets no mark if they want the special name.

Perimeter of a Regular Polygon

Exams also ask for the perimeter of a regular polygon. All its sides are equal, so you never need to add them one by one.

Formula

P = n \times s

$P$ is the perimeter (the distance all the way round), $n$ is the number of sides, and $s$ is the length of one side.

1. A regular pentagon has sides of 8 cm. Find its perimeter.

Worked example

1
$n = 5$ — A pentagon has 5 sides. The name tells you n.
2
$P = 5 \times 8$ — Regular means all 5 sides are 8 cm, so multiply instead of adding 8 five times.
3
$P = 40 cm$ — 5 × 8 = 40. A perimeter is a length, so give the units: cm.

2. A regular hexagon has the same perimeter as a regular pentagon with sides of 12 cm. Find the length of one side of the hexagon.

Worked example

1
$P = 5 \times 12 = 60 cm$ — Find the perimeter you know first: the pentagon has 5 sides of 12 cm.
2
$6 \times s = 60$ — The hexagon's perimeter is also 60 cm, and it has 6 equal sides.
3
$s = 60 \div 6 = 10 cm$ — Divide by 6 to undo the × 6. So each side is 10 cm.
4
$6 \times 10 = 60 ✓$ — Check: 6 sides of 10 cm make 60 cm, the same as the pentagon.

Key idea

Write the line 5 × 12 = 60 even if it feels obvious. That line alone earns a mark for working, even if a later step slips.

Common mistake

Using the wrong number of sides. Name the shape first, then write n: hexagon 6, heptagon 7, octagon 8.

Which Method? Read the Question

Most polygon questions start by counting sides.

You see	You do
Name this polygon	count the sides, give the name
A 5-sided polygon is called...	pentagon
Name this quadrilateral	Quadrilateral Properties
Name this triangle	Classifying Triangles
Perimeter of a regular polygon	number of sides × one side
Angle sum or each angle	Interior and Exterior Angles of Polygons

Key idea

Spell the name carefully. Octagon, not octogon.

Practise polygons now

Interactive visual aids, then real past-paper questions marked on your working like the exam. Free to start.

Practise free on Lemmara

Real past-paper questions on polygons

Each with a full worked solution.

All 24 questions on this topic →

Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education or Pearson Edexcel. The lessons and worked examples are Lemmara’s own.