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Assuming that there is nothing strange going on (e.g. sloppy surveying) there are 40 acres in the quarter-quarter section.

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Q: How many acres in the SW quarter of the SE quarter of section 1?
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What are township range and sections on a map and how do I figure out the quarter section of the section?

; Quarter Section: One quarter of the 640 acre Section, each Quarter Section being 160 acres, named Northeast (NE/4), Southeast (SE/4), Northwest (NW/4), and Southwest Quarters (SW/4). ; Exception I: Quarter Sections designated as Lotsmay (and usually do) vary in acreage. Due to the curvature of the earth, some Townships contain Sections on the North and/or West sides in which the exterior (perimeter) of the Quarter of a Quarter Section - e.g. N/2 (North half) NE/4 NE/4 may be designated as a Lot. If so each half along the perimeter of th Quarter of a Quarter along that side of the Section would be numbered as a Lot. E.g. N/2 NE/4 NE/4 = Lot 1, N/2 NW/4 NE/4 = Lot 2, N/2 NE/4 NW/4 = Lot 3, etc. Therefore that Quarter of a Quarter Section will not contain 40 square acres, the Quarter Section will not contain 160 square acres and the Section will not contain 640 square acres. ; Exception II: A river may change course and "take" land formerly surveyed as being part of a given Quarter Section, thus changing the areage. ; Section: Basic unit of the system, a square tract one mile from East to West and one mile from North to South containing 640 acres. ; Township: 36 Sections arranged in a 6 by 6 array, measuring 6 miles by 6 miles. Sections are numbered beginning with the Northeast-most Section, proceeding West to 6, then South along the West edge of the Township and back to the East for Sections 7 - 12, etc. ; Range: Assigned to a Township by measuring East or West of a Principal Meridian ; Range Lines: North to South lines which mark Township boundaries ; Township Lines: East to west lines which mark Township boundaries ; Principal Meridian: Reference or beginning point for measuring East or West ranges.

Why are farms cut into 40 acre pieces?

Because when land in the US was originally being surveyed, they decided to break it up into one-square-mile blocks, or sections, of 640 acres. Those were broken up into quarter sections of 160 acres each, and those were divided down into 40 acre "quarter-of-a-quarter" pieces. This is why land descriptions are frequently seen described as "... the SE 1/4 of the NE 1/4 of section 12...", for example. Because the earth is spherical, not all of the blocks are exactly 40 acres. Due to the necessity for what is called "correction lines", some of the blocks have to be slightly less than 40 acres.

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