What is a heptagon?
A heptagon is a flat shape with seven straight sides and seven corners.
The answer
A regular heptagon has 7 sides, 7 vertices, no parallel sides and 7 lines of symmetry. The angles inside a heptagon add up to 900°.
Heptagon diagram and properties
| Property | Regular |
|---|---|
| Sides | 7 |
| Vertices (corners) | 7 |
| Angles add up to | 900° |
| Each angle | about 128.6° |
| Right angles | 0 |
| Pairs of parallel sidesIrregular heptagons can have some. | 0 |
| Lines of symmetryAn irregular heptagon may have fewer. | 7 |
Key facts about the heptagon
- The angles inside any heptagon add up to 900°.
- In a regular heptagon each angle is about 128.6°. It does not come out as a whole number: 900 ÷ 7 = 128 remainder 4.
- A regular heptagon has no parallel sides, because it has an odd number of sides.
- It is sometimes called a septagon, from the Latin for seven.
Where you see it
The UK 50p and 20p coins have seven sides. Their edges are gently curved so each coin is the same width whichever way it is measured, which lets machines check it.
The common mistake
Mixing up heptagon (7 sides) and hexagon (6 sides). "Hept" sounds a little like "sept", as in September, which was once the seventh month.
An 11+ style question
What do the angles inside a heptagon add up to?
Answer: 900°
- Pick one corner and draw lines to every other corner you can. A heptagon splits into 7 − 2 = 5 triangles.
- Each triangle has 180°, so 5 × 180 = 900°.
Related shapes and skills
More shapes
Questions parents ask
How many sides and vertices does a heptagon have?
A heptagon has 7 straight sides and 7 vertices (corners). Its angles add up to 900°.
How many lines of symmetry does a heptagon have?
A regular heptagon has 7 lines of symmetry. An irregular heptagon may have fewer.
Is a 50p coin a heptagon?
Very nearly. It has seven sides and seven corners, but each side bulges out slightly so the coin is the same width whichever way it is measured. In maths it is called a curved or Reuleaux heptagon.
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.