COMPUTATION AND OFFICE WORK 37 



That is a very undesirable thing to do, however, as it in- 

 fringes on the tests which serve to verify the work. 



2. AREA 



Rectangles. The woodsman in his land work has 

 most frequently to do with rectangular figures, and com- 

 putation of area is simple. If the average of the chained 

 east and west sides of a rectangular piece of land is 201 

 rods or 50.25 chains, and the north and south dimension 

 40 chains, the area equals 50.25 X 40 -f- 10 (the number of 

 square chains in an acre), or 201 acres. So with a rect- 

 angular piece of any dimensions. 



Area by Triangles. The area of a triangle of known 

 base and altitude is half the product of these dimensions, 

 and an irregular figure when plotted may be cut into tri- 

 angles, the dimensions of each measured, and the areas 

 computed. The same process in case of necessity may 

 be performed on the ground. 



When, as is frequently the case, it is easier to obtain the 

 three sides of a triangle than the base and altitude, the area 

 may be obtained from the formula 



Area = -\A'( 5 ~ a ) ( s ~ &) ( s ~ c ) 

 where a, b, and c are the three sides and s is half their sum. 



Or, lastly, an irregular figure when plotted may be re- 

 duced graphically to the triangular form and the area ob- 

 tained at one computation by either of the methods just 

 given. 



The relations between units of distance and of area are 

 given on page 19. 



By Offsets. In surveying around the borders of a body 

 of water, and in some cases when the exact border of a 

 property presents great difficulties, it is customary to run 

 as near the border as is practicable and to take rectangu- 

 lar offsets to it at selected intervals along the line. These 

 offsets should be measured to angles in the border, or 

 placed near enough together so that the border between 

 offsets may be considered a straight line. The area of 

 the figure between each two offsets may then be computed 

 by multiplying the distance along the base by half the 

 sum of the two offsets. 



