Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Hexagon Cut Out

The diagram shows an irregular hexagon with interior angles all equal to 120 degrees made by cutting the corners off a piece of card in the shape of an equilateral triangle with sides of length 20 units.

An identical hexagon could also be made by cutting the corners off a different equilateral triangle.

What is the side length of this triangle?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

## You may also like

### Cube Paths

### Coins on a Plate

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 11 to 14

ShortChallenge Level

- Problem
- Solutions

The diagram shows an irregular hexagon with interior angles all equal to 120 degrees made by cutting the corners off a piece of card in the shape of an equilateral triangle with sides of length 20 units.

An identical hexagon could also be made by cutting the corners off a different equilateral triangle.

What is the side length of this triangle?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.