I'm going to take a quick stab at this, but hopefully you'll post the correct answer if/when you find it.

Okay, we have 36m of fencing to use and the person wants to build a rectangle.

So, the person can rectangles of the following dimensions:

1m width by 17m length

2m width by 16m length

3m width by 15m length

4m width by 14m length

5m width by 13m length

6m width by 12m length

7m width by 11m length

8m width by 10m length

Those are all of the possible dimensions that can be used to create a rectangular enclose whose perimeter is 36m.

We're looking for the expected area of the enclosure, which means you're looking for the average area from all of the possible enclosure sizes listed above. So we calculate the area for each of the dimensions listed above:

So, the expected or average area would simply be:

I'm fairly confident that this is the correct way of approaching the problem, but if it is wrong I'd love to see the proper way to do it. Thanks