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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Square Areas

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An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?