CHAPTER V 

 COMPUTING AREAS 



Method of Computing Areas. One of the primary objects 

 in making a farm survey is the determination of the areas of 

 fields and plats. The computation of areas as here described 

 is dependent upon a knowledge of mensuration and geometry. 

 The general plan to be followed is to divide the tract into 

 simple or primary figures whose areas can be easily calcu- 

 lated. These familiar rules of mensuration will now be 

 reviewed. 



Rectangles. If a tract of land is rectangular in shape, 

 its area is found by multiplying its length by its breadth. 

 Triangles. If a piece of ground is in the form of a tri- 

 angle, its area may be obtained by either of the following 

 rules: (1) If the length of one side, and the perpendicular 

 distance from this side to the opposite angle, or the altitude 

 of the triangle, are known, the area is one-half the product 

 of the known side as the base, times the altitude. (2) If all 



three sides of a triangle are measured, 

 then the area may be obtained by 

 adding the lengths of the three sides 

 and dividing the sum by two; from 

 Fig. i6. this half sum subtract the length of 



each side in turn; multiply together this half sum and the 

 three remainders; the square root of the product equals the 

 desired area. Thus, if a, b, and c are three sides of a triangle, 



, a + b+c ., 

 and s = , then 



S >> 



area = 1/ s (s-a) (s-b) (s-c) 



- 4/-/ K ti 6±*<* 



