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?

Find the ratio of the outer shaded area to the inner area for a six
pointed star and an eight pointed star.

Tilted Aquarium

Age 14 to 16 Short Challenge Level

The rectangular base of an aquarium is 2 metres by 3 metres, and its height is 1.5 metres. The aquarium is tilted along AB (so that the side AB is still along the floor) until the water completely covers the face ABCD. At this point, it also covers 80% of the 2 by 3 metre base.

What is the depth of the water when the aquarium is level?