The area contained by the traverse lines can be calculated only when the closed traverse has been adjusted by the Bowditch method. The method most frequently applied is the Area by coordinates method. The foundation of the method is the summation of trapezoidal areas- the trapezoids that are created between the datum and the individual traverse sides. See the diagram below left.

The area is calculated with the following formula:

½(N₁·E₂ - N₂·E₁ + N₂·E₃ - N₃·E₂ + N₃·E₄ - N₄·E₃ - N₁·E₄ + N₄·E₁)

The equation is best remembered and laid out as the matrix form shown above right.

The steps to calculate Area by Coordinates

1. Construct matrix as shown on the left.
2. Make sure that the start point is repeated as a last point.
3. Calculate and sum the +ve and -ve products.
4. Subtract the -ve product from the +ve product.
5. Divide the result by 2 and the absolute value is the shape area.

A good interactive Area by coordinates tool is available on the Edumine© site. Once there click the Area of an irregular polygon link. Click here to go to the page.

If you would like to inspect the Edumine© site from its homepage click here.