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This might be a bit of a cheap answer, but:

Of all shapes, circles have the highest area/perimeter ratio; that is, they have a maximum area for a minimum perimeter.

1000 = circumference = 2 pi r

r = about 159.155 m

area = pi (r squared) = about 79577.538 sq. m

using pi = 3.14159

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Q: What is the maximum area of a shape with a perimeter of 1000 m?
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