How do you measure the number of acres in a section?

About 25

An acre is a unit of area not of length, so I can see why you are having trouble conceptualizing it.

ok
A section is 640 acres or one square mile. So imagine if we divide the section into quadrants. The first quadrant is now 160 acres or one-quarter square mile, so this segment is 2,640 feet by 2,640 feet, is that right?
So I guess my problem is that while you can have 640 acres in a square mile, those 640 acres can not be configured into the square mile AS SQUARES. Is that right?

Or the proverbial “40 acres and a mule” was a section of land 1/4 mile by 1/4 mile, or 1,742,700 square feet, but each acre would be a rectangle and not a perfect square?

SRM

1/4 of a mile by 1/4 of a mile is 160 acres, not 40.

sqrt(40) is not a whole number, so no matter how hard you try, you cannot lay out 40 squares in a square.

the same area of 40 acres is in a 1/8 mile bye 1/8 mile patch, though.

Thanks, it was the fact that you couldn’t lay out the acres, whether 40, 160 or 640 into squares that was throwing me.
SRM