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A mensuration formula is simply a formula for computing the length-related properties of an object (such as Area, Circumradius, etc., of a Polygon) based on other known lengths, areas, etc. Beyer (1987) gives a collection of such formulas for various plane and solid geometric figures.
References
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 121-133, 1987.