How many acres are in the corners of a quarter section of irrigated land?

Question

How many acres are in the corners of a quarter section of irrigated land?

Answer 1

I have to presume that the irrigation is done by a rotating system from the center of the quarter section, otherwise I have no idea how one would calculate this.  

What you have is a square with a circle inside it, and you want to know the area of the square that isn't in that circle.

A quarter section is 160 acres, being one half of a mile square.   That gives it a radius of 1320 feet.  The area of that circle is Pi * the square of the radius, or 5,473,924 square feet.   The area of the square is 6,969,600 feet.  Square minus circle is 1,495,676 feet,  or just over 34 acres.  

That presumes a single circular irrigation system for the entire 160 acres.  The answer is probably different if you have four irrigation systems for each of the 40 acres, but the methodology for calculating would be the same, only the scale would be different.