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 dots are one unit apart. What is the area of the region common to both the triangle and the square (in square units)?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.