An Unusual Shape

Can you maximise the area available to a grazing goat?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
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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:

Image
An Unusual Shape

 

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?