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 989.900

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 is 1857 m^2.

Compute the area (square meters and up to 4 decimal places) of corner "C"

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.