Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
Can you work out the area of the inner square and give an explanation of how you did it?
Can you use the fact that a regular hexagon comprises equilateral triangles?
Can you see a connection between the area of the equilateral triangle and the hexagon?