Figure 7-23.—Area from double parallel distances.The double area of DA is523.62 x 591.64 = 309,794.54 square feet.The difference between the sum of the minus doubleareas and the sum of the plus double areas is the doublearea which is 647,907.39 square feet. The area is onehalf of this, or 323,953.69 square feet. Land area isgenerally expressed in acres. There are 43,560 squarefeet in 1 acre; therefore, the area in acres isAREA BY DOUBLE PARALLEL DISTANCE.—You can check the accuracy of the area computation ofa DMD by computing the same area from doubleparallel distances (DPD).As shown in figure 7-22, the parallel distance of atraverse line is the north-to-south distance from themidpoint of the line to a reference parallel. The referenceparallel is the parallel passing through the mostsoutherly traverse station.You can see that the solution for parallel distance isthe same as the one used for meridian distance, exceptthat to compute parallel distance you use latitude insteadof departure. The parallel distance of the initial traverseline (which is DA in this case) equals one half of thelatitude. The parallel distance of the next line, AB, equalsthe parallel distance of the preceding line, DA, plus onehalf of the latitude of the preceding line DA, plus onehalf of the latitude of line AB itself.It follows from the above that the DPD of the initialtraverse line DA equals the latitude of the line. The DPDof the next line, AB, equals the DPD of the precedingline, DA, plus the latitude of the preceding line, DA, plusthe latitude of the line AB itself. The solution for area isthe same as for area by meridian distance except that,for the double area of each traverse line, you multiplythe DPD by the departure instead of multiplying theDMD by the latitude.Figure 7-23 shows entries for the computation of thearea of DPD for the traverse we are working on. Notethat the result is identical with that obtained by thecomputation of the DMD.AREA FROM COORDINATES.— Before weexplain the method of computing area from coordinates,let us set coordinates for the stations of the traverse weare working on. To avoid using negative coordinates, wewill measure Y coordinates from an X axis passingthrough the most southerly station and X coordinatesfrom a Y axis passing through the most westerly station,as shown in figure 7-24.Figure 7-24.—Computations of a closed traverse by coordinatemethod.7-17