SURVEYING 37 



Second Method: If the 

 side of the irregular field 

 is not of such a character 

 as to be readily divided 

 into large trapezoids, then 

 the offsets may be taken 

 at regular intervals along the base line. 



If d be the regular interval between offsets then the area of the 

 trapezoid whose sides are h and h ' is equal to one-half their sum mul- 

 tiplied by d, or 



AREA ABCD = %d (h+h ') 



PROBLEMS 



1. What is the area in acres of a rectangular field whose length is 

 1320 feet and whose width is 347^ feet? 



2. How many acres in a field 80 chains long and 13.25 chains wide? 



3. What is the area in square feet of a triangular piece of ground, if 

 the length of one side is 339 feet and the altitude on this side as a base is 

 92 feet? 



4. The length of the sides of a tract of land in the form of a tri- 

 angle are 220,310, and 343 feet. What is the area in acres? 



5. The four sides of a trapezium are 420, 417, 380 and 375 feet 

 taken in order around the field, the diagonal from the corner between 

 the 417 and the 380 foot sides to the opposite corner is 528 feet. Find 

 the number of acres in the tract. 



6. Find the acre area of a road 66 feet wide and 3960 feet long. 



7. Find the area in square feet of a tract of land with an irregular 

 shaped side if offsets taken at the regular interval of 50 feet are 0, 25, 

 30, 28 and 50 feet, respectively. 



8. How many rows of corn 3 feet 6 inches apart can be planted in 

 a field 20 rods wide? How many hills of corn 3 feet 6 inches apart will 

 there be in the field if it be 80 rods long? 



9. How many apple trees 20 feet apart may be planted hi a 1-acre 

 tract in the form of a square? Try a different arrangement of the trees. 



10. At this point the student should be prepared to take up the 

 problem of surveying, mapping, and calculating the area of certain 

 tracts of land, as the school house yards, lot, field, or even whole farms 



