Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Cosines Rule

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

Squ-areas

Age 14 to 16Challenge Level

The diagram shows three squares on the sides of a triangle $ABC$.

Their areas are respectively 18 000, 20 000 and 26 000 square centimetres.

If the squares are joined, three more triangular areas are enclosed. What is the area of this convex hexagon?