Problem of the week: Advanced Mathematics Problems: Areas

An existing rectangular parcel of land was measured many years ago with a Gunter's chain and was found to contain 40 ac. The original surveyor noted later that the chain used to make the measurements was one link too short. Assuming that the error was evenly distributed throughout the measuring, what was the area of the parcel?

A. 39.20 ac
B. 39.60 ac
C. 40.40 ac
D. 40.80 ac

Solution:Although the dimensions of the rectangle are not known, the error can be calculated. The original surveyor measured the length, x, and depth, y, of the rectangle and found that xy = 40 acres. Since the chain was missing one of its 100 links, however, the length was actually 0.99x and the depth 0.99y. Therefore, the correct area is

A = (0.99x)(0.99y) = 0.9801xy
= (0.9801)(40)
= 39.20 ac

The same result will be found if the parcel is presumed to be rectangular but not square.

The answer is (A).

This is problem 15(2-3) from the NEW third edition of “Surveying Solved Problems for the FS and PS Exams” by Jan Van Sickle, PLS (formerly "1001 Solved Surveying Fundamentals Problems"). Reprinted with permission from “Surveying Solved Problems for the FS and PS Exams” by Jan Van Sickle, PLS (2008 Professional Publications Inc.). For details on this and other FLS exam-prep books, call 800/426-1178 or

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