The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
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
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?
This problem is taken from the UKMT Mathematical Challenges.