Minimum Area Enclosed

Calculus Level 3

Suppose you have 1000 meters of fencing material. You set out to build a closed circular fence and a closed square fence, as shown above. The circular fence is partitioned into 4 quadrants by two perpendicular diameter sections.

If all of the fencing material must be used, what is the minimum possible combined area enclosed by the two fences (in square meters, to the nearest square meter)?

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