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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?

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.

Dividing the Field

Age 14 to 16
Challenge Level

A farmer has a field which is the shape of a trapezium as illustrated below.

To increase his profits he wishes to grow two different crops.
To do this he would like to divide the field into two trapeziums, each of equal area.

How could he do this?