What is a decagon?
A decagon is a flat shape with ten straight sides and ten corners.
The answer
A regular decagon has 10 sides, 10 vertices, 5 pairs of parallel sides and 10 lines of symmetry. The angles inside a decagon add up to 1440°.
Decagon diagram and properties
| Property | Regular |
|---|---|
| Sides | 10 |
| Vertices (corners) | 10 |
| Angles add up to | 1440° |
| Each angle | 144° |
| Right angles | 0 |
| Pairs of parallel sidesIrregular decagons may have fewer. | 5 |
| Lines of symmetryAn irregular decagon may have fewer. | 10 |
Key facts about the decagon
- The angles inside any decagon add up to 1440°.
- In a regular decagon every angle is 144°.
- A regular decagon has 5 pairs of parallel sides.
- "Dec" means ten, as in decade (ten years) and decimal (counting in tens).
Where you see it
Decagons are rare in everyday life, so a decagon in a question tests the angle rule rather than a remembered fact.
The common mistake
Forgetting the angle rule and guessing. Split the decagon into triangles from one corner: there are always 2 fewer triangles than sides, so 8 triangles here.
An 11+ style question
A regular decagon has sides of 4.5 cm. What is its perimeter?
Answer: 45 cm
- A regular decagon has 10 equal sides.
- 4.5 × 10 = 45, so the perimeter is 45 cm.
Related shapes and skills
More shapes
Questions parents ask
How many sides and vertices does a decagon have?
A decagon has 10 straight sides and 10 vertices (corners). Its angles add up to 1440°.
How many lines of symmetry does a decagon have?
A regular decagon has 10 lines of symmetry. An irregular decagon may have fewer.
What do the angles in a decagon add up to?
1440°. A decagon splits into 8 triangles from one corner, and 8 × 180 = 1440.
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.