### 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.

# Polygon Rings

##### Age 11 to 14 Challenge Level:
Here is a pattern made of regular pentagons:

If the pattern continued, do you think it will form a complete loop or will the pentagons overlap?
Try it using the Tessellation Interactivity below.
If you've never used the interactivity before, there are some instructions and a video.

Once you've had a chance to explore, here are some questions you might like to consider.

How many pentagons form a ring?
How many decagons would form a ring?
Why do they fit together so neatly without overlapping or leaving a gap?