70 ANGULAR SURVEYING 



Let it be required to divide the trapezoid A BCD, Fig. 1, into 

 two parts whose areas Si and 52 are to be in the ratio . In 



solving this problem, it may be necessary to find the length x of 

 the dividing line EF, the distances AE and ED, and the altitudes 



FIG. 1 



hi and ht. The following formulas are used, the notation being 

 shown in the illustration: 



DE = 



m-\-n 

 a(x-h) 



h(bi-x-) 

 hi = 



h(x-bi) 



and 2 



These formulas can be applied to a triangular tract, by taking 

 the upper base &z as zero ; then , ntbt 1 = 0. 



EXAMPLE. Suppose that the trapezoid A BCD, Fig. 1, 

 represents a tract of land in which DC = 50 ch., .4.8=100 ch., 

 AD = 47.50 ch., and A = 35 ch., and that the tract is to be so 

 divided by the line EF that the parts will be as 3 and 2, respec- 

 tively , that is , = - . Required , EF and DE. 

 ft 2 



