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 = V s(s — a) (s — b) (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 betw r een 
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 
ium of the two offsets. 
