What is an octagon?
An octagon is a flat shape with eight straight sides and eight corners.
The answer
A regular octagon has 8 sides, 8 vertices, 4 pairs of parallel sides and 8 lines of symmetry. The angles inside an octagon add up to 1080°.
Octagon diagram and properties
| Property | Regular |
|---|---|
| Sides | 8 |
| Vertices (corners) | 8 |
| Angles add up to | 1080° |
| Each angle | 135° |
| Right angles | 0 |
| Pairs of parallel sidesIrregular octagons may have fewer. | 4 |
| Lines of symmetryAn irregular octagon may have fewer. | 8 |
Key facts about the octagon
- The angles inside any octagon add up to 1080°.
- In a regular octagon every angle is 135°.
- A regular octagon has 4 pairs of parallel sides: each side is parallel to the one opposite it.
- An octopus has eight arms, which is a handy way to remember "oct" means eight.
Where you see it
A STOP sign is a regular octagon. So are some umbrellas seen from above and many garden gazebos.
The common mistake
Saying a regular octagon has 16 lines of symmetry by counting both ends of each line. There are 8: 4 through opposite corners and 4 through the middles of opposite sides.
An 11+ style question
A regular octagon has a perimeter of 64 cm. How long is each side?
Answer: 8 cm
- A regular octagon has 8 equal sides.
- 64 ÷ 8 = 8, so each side is 8 cm.
Related shapes and skills
More shapes
Questions parents ask
How many sides and vertices does an octagon have?
An octagon has 8 straight sides and 8 vertices (corners). Its angles add up to 1080°.
How many lines of symmetry does an octagon have?
A regular octagon has 8 lines of symmetry. An irregular octagon may have fewer.
What is each angle in a regular octagon?
135°. The angles add up to (8 − 2) × 180 = 1080°, and 1080 ÷ 8 = 135.
Shape questions are quick marks in the 11+
Angles, symmetry, nets and 3D shapes come up in 11+ maths and non-verbal reasoning. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.