Question

A five-sided closed field traverse has the following distances in meters: AB = 51.766; BC = 26.947; CD = 37.070; DE = 35.292; EA = 19.192. The adjusted angles are as follows: A = 101°03′19″; B = 101°41′49″; C = 102°22′03″; D = 115°57′20″; E = 118°55′29″. The bearing of AB is N 73°00′00″ E. BC is in the S.E. quadrant.The coordinates of the five(5) corners of the traverse have been computed to be as follows: Corner "A" X Coordinate 1000.000 Y Coordinate 1000.000 Corner "B" X Coordinate 1050.019 Y Coordinate 1013.314 Corner "C" X Coordinate 1062.085 Y Coordinate 989.218 Corner "D" X Coordinate 1033.262 Y Coordinate 965.900 Corner "E" X Coordinate 1001.292 Y Coordinate 980.852 The area of the traverse using the coordinate method is 1,857 Square meters. If you used the area computation method we used in class and on the homeworks, the computed number using coordinate method for area computation for corner "C" is_______? Your answer will be in square meters to four (4) decimal place accuracy.

Answer 1

In Co-ordinate method of area computation, we first write the Y co-ordinates and X co-ordinates as follows:-

Computations are done as under:

P = product along dashed line:

         B : 1000 * 1013.314 = 1013314

        C : 1050.019 * 989.218 = 1038697.695

        D : 1062.085 * 965.900 = 1025867.902

        E : 1033.262 * 980.852 = 1013477.099

        A : 1001.292 * 1000 = 1011292

Q = Product along solid line:

       B : 1000 * 1050.019 = 1050019

        C : 1013.314 * 1062.085 = 1076225.6

        D : 989.218 * 1033.262 = 1022121.369

        E : 965.900 * 1001.292 = 96147.9428

        A : 980.852 * 1000 = 980852

Computed Number at corners: P-Q

       B : 1013314-10550019 = -36705

      C : 1038697.695-1076225.6=-37527.905

       D : 1025867.902-1022121.369=3746.33

       E : 1013477.099-96147.9428=46329.1562

     A : 1011292-980852=20440

Once computed numbers are calculated, we take there sum:

Sum = -36705-37527.905+3746.33+46329.1562+20440= -3717.4188

We then take the absolute value of the sum = abs(-3717.4188) = 3717.4188

The area will be half the value of the absolute sum = 3717.4188/2 = 1858.71 sq. meter

Given area = 1857. Hence, our computed area is very close to given value.

The question asks for the computed number at C which is -37527.905. The computed number to be reported in square meters is 37527.905 sq. meters.