SURVEYING 



35 



Fig. 17. 



Parallelogram. (Fig. 17.) The 

 area of a parallelogram, a four-sided 

 figure with opposite sides parallel, is 

 equal to the product of one of its sides 

 and the perpendicular distance be- 

 tween it and the opposite parallel side. 



Trapezoid. (Fig. 18.) This is a 

 four-sided figure with two sides par- 

 allel. The area is equal to the pro- 

 duct of one-half the sum of the parallel 

 sides by the perpendicular distance between them. 



a+b 



Area = 



Xh. 



Fig. 19. 



where a and b are the two parallel sides, and h the perpendicular 

 distance between them. 



Trapeziums (Fig. 19) are quadrilateral figures, no two of 

 whose sides are parallel. A practical 

 way to obtain the area of a field of 

 this shape is to measure a diagonal 

 dividing the field into two triangles 

 whose areas may be calculated. It 

 is to be noted that averaging opposite 

 sides and taking their product will 

 not give the area. 



Area abcd = area ACD+area abc. 



Figures With Many Sides. First 

 Method: (Figs. 20 and 21.) A many- 

 sided piece of land may be likewise 

 divided in triangles and its area ob- 

 tained in the way described for tra- 

 pezium. The triangles may be formed about one of the 

 corners of the figure, or about a point wholly within the 



Fig. 20. 



