Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
A man paved a square courtyard and then decided that it was too
small. He took up the tiles, bought 100 more and used them to pave
another square courtyard. How many tiles did he use altogether?
Can you work out the area of the inner square and give an
explanation of how you did it?
How many different squares can be drawn in total by joining the dots with line segments in the part of the square lattice shown below?
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.