trapezoids. Then, by computing the area of eachtriangle and trapezoid and determining the sum of theareas, you obtain the area of the polygon.Take, for example, the plot of station 305 + 00shown in figure 10-4.Figure 10-5 illustrates how thisfigure can be resolved into two triangles, ABH andDFE, and two trapezoids, BCGH and CGFD. For eachof these figures, the approximate dimensions havebeen determined by the scale of the plot. From yourknowledge of mathematics, you know that the area ofeach triangle can be determined using the followingformula:Where:s = one half of the perimeter of the triangle,and that for each trapezoid, you can calculate the areausing the formula:When the above formulas are applied and the sumof the results are determined, you find that the totalarea of the cross section at station 305 is 509.9square feet.AREA BY FORMULA.— A regular section areafor a three-level section can be more exactlydetermined by applying the following formula:Figure 10-4.—A cross section plotted on cross-section paper.Figure 10-5.—Cross section resolved into triangles and trapezoids.10-8
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