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A square plot of ground measuring 12 acres would encompass approximately 2925 linear feet of fence-line.
If the area is a square then a minimum of 1,104.4 feet of fencing would be needed.
If the shape of the area is a square, it would take 1,181 feet of fencing for the perimeter. If the area is a circle, you will need 1,046 feet of fencing.
You can't tell the linear dimensions from the area. There are an infinite number of shapes that all enclose 40 acres but have different linear dimensions. The smallest possible straight dimensions that can enclose 40 acres occur if the field is square. Each side would be 1,320 feet, and you'd need exactly 1 mile of fence to enclose it. But if some developer owned a rectangular piece of land that was 330-ft wide and 1 mile long, his land would also measure 40 acres, but it would take 2-1/4 miles of fence to enclose it.
It depends on what kind of animal you are trying to fence in (or out). For an average cattle pasture, I prefer setting them 10 feet apart, so you would need about 150 T-posts. I still prefer setting three six-inch treated wooden posts for each corner; they will hold up better to the tensioning of the fence/barb wire.