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Imagine you had $40$ one-metre sections of fencing.

What is the largest rectangular area of land you could fence off?

Now imagine you could build your fence up against a wall, so you only need to use the fence for three sides of the enclosure:


What is the largest area you can fence off now?

Now imagine you can attach the fence to the wall shown below, at the point marked X.
L shaped enclosure

What is the largest area you can fence off now?


Extension
Could you enclose even greater areas if you had $40$m of flexible wire fencing that could fence off curves as well as straight lines?