What is a pentagon?
A pentagon is a flat shape with five straight sides and five corners.
The answer
A regular pentagon has 5 sides, 5 vertices, no parallel sides and 5 lines of symmetry. The angles inside a pentagon add up to 540°.
Pentagon diagram and properties
| Property | Regular |
|---|---|
| Sides | 5 |
| Vertices (corners) | 5 |
| Angles add up to | 540° |
| Each angle | 108° |
| Right angles | 0 |
| Pairs of parallel sidesIrregular pentagons can have some. | 0 |
| Lines of symmetryAn irregular pentagon may have 1 or none. | 5 |
Key facts about the pentagon
- The angles inside any pentagon add up to 540°.
- In a regular pentagon every angle is 108°.
- A regular pentagon has no parallel sides, because it has an odd number of sides.
- The word comes from the Greek "pente", meaning five.
Where you see it
Draw a house as a square with a triangle roof and the outline is a pentagon. It is irregular, with one line of symmetry.
The common mistake
Thinking only the regular shape counts. Any flat shape with five straight sides is a pentagon, even if the sides are all different lengths.
An 11+ style question
What is the size of each angle in a regular pentagon?
Answer: 108°
- The angles in a pentagon add up to (5 − 2) × 180 = 540°.
- A regular pentagon has 5 equal angles, so 540 ÷ 5 = 108°.
Related shapes and skills
More shapes
Questions parents ask
How many sides and vertices does a pentagon have?
A pentagon has 5 straight sides and 5 vertices (corners). Its angles add up to 540°.
How many lines of symmetry does a pentagon have?
A regular pentagon has 5 lines of symmetry. An irregular pentagon may have 1 or none.
Can a pentagon have a right angle?
Yes, an irregular one can. The house shape, a square with a triangle on top, has two right angles at the bottom. A regular pentagon has none.
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.