3. Examples
Although we carried an additional digit in all previous computations, we'll carry a few more extra here. We'll discuss the area error at the end of the chapter but for now we want to overcompute the area accuracy then report it to an appropriate resolution after we analyze it. If we don't carry additional digits, we could easily increase error due to rounding. To be on the safe side, we'll carry the computations to 0.1 which should be less than the expected error.
a. Example 1
Figure G7 is a continuation of the Bearing Traverse example we have been using in the past few chapters.


Figure G7 Example 1 Traverse 
Step (1) Start at point A and going clockwise around the traverse list the coordinates:
Point 
N (ft) 
E (ft) 

A 
500.000 
2000.000 

B 
323.614 
1561.426 

C 
526.996 
1488.321 

D 
719.336 
1686.956 

A 
500.000 
2000.000 
remember to return to A 
Step (2) Cross multiply in one direction:
Point 
N (ft) 
E (ft) 
(), sq ft 

A 
500.000 
2000.000 
647,228.0 

B 
323.614 
1561.426 
822,865.2 

C 
526.996 
1488.321 
1,070,602.9 

D 
719.336 
1686.956 
843,478.0 

A 
500.000 
2000.000 







Step (3) Cross multiply in the other direction
Point 
N (ft) 
E (ft) 
(), sq ft 
(), sq ft 
A 
500.000 
2000.000 
647,228.0 

B 
323.614 
1561.426 
822,865.2 
780,713.0 
C 
526.996 
1488.321 
1,070,602.9 
481,641.5 
D 
719.336 
1686.956 
843,478.0 
889,019.1 
A 
500.000 
2000.000 
1,438,672.0 
Step (4) Add up the columns
Point 
N (ft) 
E (ft) 
(), sq ft 
(), sq ft 
A 
500.000 
2000.000 
647,228.0 

B 
323.614 
1561.426 
822,865.2 
780,713.0 
C 
526.996 
1488.321 
1,070,602.9 
481,641.5 
D 
719.336 
1686.956 
843,478.0 
889,019.1 
A 
500.000 
2000.000 
1,438,672.0 



sums: 
3,384,174.1 
3,590,045.6 
Step (5) Using Equation G3 compute the area
Until we discuss area accuracy more fully, we'll state the area as 102,935.8 sq ft.
There's nothing magical or sacred about point A. We could have stated our list at point C and traveled counterclockwise around the traverse. As long as we remember to repeat the initial point at the bottom of the list, we will come up with the same area although one could be positive and the other negative.
b. Example 2
Figure G8 shows the Crossing Traverse we've been using as another running example.


Figure G8 Crossing Traverse 
With a crossing traverse, one must be careful when listing the coordinates. In this case, if you list the coordinates along the original traverse path, EFGHE, you will be able to compute an area but it will be nonsensical. The traverse turns itself inside out.
Recall that this survey was on a foursided parcel having two obstructed lines, Figure G9.
Figure G9 
We want the the area of the parcel, not the traverse.
Step (1) Start at point E and going clockwise around the parcel, list the coordinates.
Point 
N (ft) 
E (ft) 

E 
1000.000 
200.000 

G 
896.890 
627.584 

F 
689.206 
532.694 

H 
692.474 
257.460 

E 
1000.000 
200.000 
remember to return to E  
Step (2)(4) Cross multiply in both directions; sum the columns.
Point 
N (ft) 
E (ft) 
(), sq ft 
(), sq ft 
E 
1000.000 
200.000 
179,378.0 

G 
896.890 
627.584 
432,534.7 
624,584.0 
F 
689.206 
532.694 
368,876.7 
477,767.9 
H 
692.474 
257.460 
257,460.0 
177,443.0 
E 
1000.000 
200.000 
138,494.8 




1,238,252.4 
1,418,289.7 
Step (5) Use Equation (G3) to compute the area