At a Glance

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

Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

Equilateral Areas

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.

Squ-areas

Age 14 to 16 Challenge 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?