Elementary Surveying - An Introduction to Geomatics (13th Edition)_部分2.pdf

310 AREA
TABLE APPROXIMATE AREA CONVERSION FACTORS
To Convert from To Multiply by
ft2 m2 (12>)2 L
m2 ft2 (>12)2 L
yd2 m2 (36>)2 L
m2 yd2 (>36)2 L
acres hectares [>( * 12)]2 L
hectares acres ( * 12>)2 L
the enclosing lines. These processes are described and illustrated in Section .
Because maps themselves are derived from field observations, methods of area
determination invariably depend on this basic source of data.
■ AREA BY DIVISION INTO SIMPLE FIGURES
A tract can usually be divided into simple geometric figures such as triangles,
rectangles, or trapezoids. The sides and angles of these figures can be observed in
the field and their individual areas calculated and example of a parcel
subdivided into triangles is shown in Figure .
F

G

102
E 69 I
H
N
D
71
257
JK


B
C
92 M

535 L
A
Figure
Area determination
by triangles.
Area by Offsets from Straight Lines 311
Formulas puting areas of rectangles and trapezoids are well known.
The area of a triangle whose lengths of sides are known can puted by the
formula
area = 2s(s - a) (s - b) (s - c) ()
= > + +
where a, b, and c are the lengths of sides of the triangle and s 1 2(a b c).
Another formula for the area of a triangle is
1
area = ab sin C ()
2
where C is the angle included between sides a and b.
The choice of whether to use Equation () or () will depend on the
triangle parts that are most conveniently determined; a decision ordinarily dictated
by the nature of the area and the type of equipment available.
■ AREA BY OFFSETS FROM STRAIGHT LINES
Irregular tracts can be reduced to a series of trapezoids by observing right-angle
offsets from points along a reference line. The reference line is usually marked by
sta