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# An Unusual Shape

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Age 11 to 14

Challenge Level

*An Unusual Shape printable sheet*

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?