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?
The area of a square inscribed in a circle with a unit radius
is, satisfyingly, $2$.
What is the area of a regular hexagon inscribed in a circle with
a unit radius?
What is the area of an equilateral triangle inscribed in a
circle with a unit radius?