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Figure  7-25.Coordinate  entries  for  computation  of  figure  7-24.
AREA BY PLANIMETER

Engineering Aid 1 - Advanced Structural engineering guide book
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Figure 7-27.—Second step for tabulated computation of figure 7-24. Figures  7-26  and  7-27  show  the  method  of determining the double area from the coordinates. First, multiply   pairs   of   diagonally   opposite   X  and  Y coordinates, as shown in figure 7-26, and determine the sum of the products. Then, multiply pairs diagonally in the opposite direction, as shown in figure 7-27, and determine  the  sum  of  the  products.  The  difference between the sums (shown in fig. 7-26) is the double area or 1,044,918.76 – 397,011.37 = 647,907.39 square feet The symbol shown beside the sum of the coordinate products is the capital Greek letter (Z) sigma In this case, it simply means sum. AREA BY TRAPEZOIDAL FORMULA.— It is often necessary to compute the area of an irregular figure, one or more of whose sides do not forma straight Figure  7-28.—Area  of  irregular  figure  by  trapezoidal  rule. line. For illustration purpose, let us assume that figure 7-28 is a parcel of land in which the south, east, and west boundaries are straight lines per pendicular to each other, but the north boundary is a meandering shoreline. To determine the area of this figure, first lay off conveniently equal intervals (in this case, 50.0-foot intervals) from the west boundary and erect perpen- diculars as shown. Measure the perpendiculars. Call the equal interval d and the perpendiculars (beginning with the west boundary and ending with the east boundary) hl through k. Now,  you  can  see  that  for  any  segment  lying between two perpendiculars, the approximate area, by the rule for determining the area of a trapezoid, equals the  product  of  d  times  the  average  between  the perpendiculars. For the most westerly segment, for example, the area is The  total  area  equals  the  sum  of  the  areas  of  the segments; therefore, since d is a factor common to each segment, the formula for the total area may be expressed as  follows: 7-19







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