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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

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Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

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A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Eight Ratios

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Oliver, from Nottingham High School, and Jonathan, both sent in very good solutions to this problem.

Here is Jonathan's solution:


Oliver's solution is below:


Well done to both Jonathan and Oliver for their excellent solutions!