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» Home » Geometry »

Trapezoidal Rule

          To find the area of the as shown in the figure, the base  is divided into number of equal intervals of width. The ordinates are accurately measured. The approximation used in this rule is to assume that each strip is equal to the area of a trapezium. Therefore
            Area of a Trapezium (Sum of parallel sides)  (perpendicular distance between the parallel sides)

Hence, the first strip, the approximate area is
For the second strip, approximate area is, and so on.
            Therefore, approximate area of
          
          
          
          
Area  width of Interval sum of first and last ordinate  + Sum of remaining ordinates


Example:
            Find the area of cross-section of a river along a line where the depths at equal intervals of m, are noted as m, respectively.
Solution:
            Width of each strip, m
            Ordinates are
            Since,
                        Area  width of Interval sum of first and last ordinate  + Sum of remaining ordinates
                                 square meter.


Example:
            Apply trapezoidal rule to find the area of a plot of land having the following dimensions:
            Ordinates:  and m
            Common distance: m
Solution:
            Given that m, m, m, m, m respectively and m
             By Trapezoidal Rule
                        Area
                                
                                 square meter.




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