How much fence to enclose the perimeter 700 acres?

Answer 1

To enclose a 700-acre square lot would require about 4.2 miles of Fencing.

The minimum perimeter is when the 700 acres are inside a circle.

area_circle = πr² → r = √(area/π)

circumference = 2πr = 2π√(area/π) = 2 × √(π × area)

1 acre = 1/640 sq mile

→ minimum perimeter = 2 × √(π × 700/640 sq miles) ≈ 3.71 miles.

The fence is at least approx 3.71 miles long. Depending upon the exact shape of the area, depends how much more than this the fence will required to be.

For example, if the 700 acres was 700 fields a chain wide by a furlong long next to each other (making 1 big field a furlong by 700 chains), the length of fence required would be 2 × (220 + 22 × 700) yds = 31240 yds = 17¾ miles long.

Answer 2

The area is not sufficient information to determine the length and width. First of all, there is no reason to suppose that the area is rectangular as opposed to circular or triangular or some other simple or complicated shape. Even if you assume that it is a rectangle, there are infinitely many possible answers: ranging from nearly square areas to extremely long very thin strips.