A square of side 8cm, is painted pink and fixed to a table.

An identical square, painted white, is placed on the table alongside the pink square, and has a point P marked one quarter of the way along the diagonal as shown.

If the white square slides once around the pink square, keeping the same orientation and always remaining in contact with the pink square, through what distance does P move?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.