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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?

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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).

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Getting an Angle

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

Subtended Angles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

If you are having difficulty with the interactivity, you may find this helpful:

* To create a rubber band for placing on your peg board, click on the colour of band that you would like to use, in the right-hand-side table.

* A new icon will appear on the screen. Drag this rubber band over to a peg on the board. Let go.

* You can now drag the rubber band to different pegs. To create another rubber band, repeat the above.

Join all the points up to the centre and look for isosceles triangles.

You may find this diagram helpful to get you started.

It is useful to note that the blue lines are all radii of the circle, and as such, are all the same length. You may want to use some algebra to help explain your proof .