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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

Because the data for this problem only mentions ratio, not length, you can imagine the diagram being scaled up or down without any of the ratio values changing. So choose one length somewhere as something convenient and then try to calculate other lengths from that.