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?
A large container holds 14 litres of a solution that is 25% antifreeze, the remainder being water. How many litres of antifreeze must be added to the container to make a solution that is 30% antifreeze?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.