Actually, since the wire is cut into two pieces (that are equal, I assume), the perimeter of the square is 5/2 meters or 250 cm. Each side of the square would then be 250/4 cm, which equals 62.5 cm. \(62.5^2\) is 3906. The total area of the square would then be 3906.25 \(cm^2\) or 0.390625 \(m^2\).
The minimum area would be 0...just don't place the wire.
I think you meant to state the question differently...
Hope this sort of helps,
- PartialMathematician