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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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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?

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Gift of Gems

Four jewellers share their stock. Can you work out the relative values of their gems?

Areas and Ratios

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This problem is in two parts. The first part provides two building blocks which will help you to solve the final challenge. These can be attempted in either order. Of course, you are welcome to go straight to the Final Challenge!

Click on a question below to get started.

Question A

Question B