# 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.