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Can you work out the area of the inner square and give an explanation of how you did it?

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Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

Bow Tie

Age 11 to 14
Challenge Level


Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling. The lengths AE and ED are 1 unit and the length CD is 2 units. The angles B and E are right angles and the angles A, C and D are 120 °.

Here is a printable copy for you to download, print and try yourself.

Here is an interactive that may help you.
Click on the grey shapes to create new tiles. You can rotate the pieces using the corner points.


Printable NRICH Roadshow resource.