# Trapezoidal Rule

To find the area of the trapezium as shown in the figure, the base is divided into 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's approximate area is

For the second strip, the approximate area is , and so on.

Therefore, the approximate area of

**Area ** **width of interval** **sum of first and last ordinate **** + sum of remaining ordinates**

__Example__:

Find the area of a 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 meters.

__Example__:

Apply the 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 the trapezoidal rule:

Area

square meters.