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'An Unusual Shape' printed from http://nrich.maths.org/
Stuart tethered his goat to one end of a $20$-foot length of rope and attached the other end of the rope to a hook fixed to the side of his shed.
When he came back the goat had eaten all the grass within its reach.
Here is a picture showing the region eaten by the goat:
Where did Stuart fix the rope?
What was the area grazed by the goat?
Could the goat have eaten more grass if the rope had been attached to a different point on the shed?
Experiment with different lengths of rope. Where should the hook be positioned each time to allow the goat to eat the maximum amount of grass?