### 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?

### Pie Cuts

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

### Getting an Angle

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

# Right Angled Octagon

##### Stage: 3 Short Challenge Level:

$6$ right angles can be achieved, as in the diagram below:

If there were seven right angles, these would be a total of $7 \times 90^\circ = 630^\circ$. The total interior angle of an octagon is $6 \times 180^\circ = 1080^\circ$, so the final angle would have to be $1080^\circ - 630^\circ = 450^\circ$. The interior angle cannot be more than $360^\circ$, so this cannot be achieved.

This problem is taken from the UKMT Mathematical Challenges.
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