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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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Contact

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

Although we have had some numerical answers sent in no one has explained their method.

Could you be the first to explain the calculation so that someone else can see how it's done and why it's right ?