### Floored

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

### Getting an Angle

How can you make an angle of 60 degrees by folding a sheet of paper twice?

### Arclets Explained

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

# Heptagon Has

##### Age 11 to 14 Short Challenge Level:

A heptagon is a seven-sided polygon. What is the greatest number of the following properties that a single heptagon can possibly possess?

• Its interior angles add up to $900$ degrees
• It has exactly four acute interior angles.
• It has no obtuse interior angles.
• All its sides are equal.
• It has exactly one line of symmetry.
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.