What is the perimeter of a property that is 640 acres by 640 acres?

Answer 1

An acre is a measure of area and has two dimensions;

640 acres by 640 acres is 409600 acres2 which has four dimensions.

Methinks you do not mean a property that is 640 acres by 640 acres.

Getting back to just 640 acres (and forgetting the "by 640 acres") as long as the shape has an area of 640 acres it doesn't matter what shape it is.

The shape with an area of 640 acres with least perimeter is a circle:

area = π x radius2

⇒ radius = √(area/π)

circumference = 2 x π x radius

= 2 x π x √(area/π)

= 2 x √(area x π)

= 2 x √(640 x 4840 sq yds x π)

≈ 6239 yds

Any other shape will have a longer perimeter - it can have any value greater than approx 6239 yards, examples a rectangle with sides:

• 2 yds and 1548800 yds will have an area of 640 acres and a perimeter of 3097604 yds;
• 1 yd and 3097600 yds will have an area of 640 acres and a perimeter of 6195202 yds.