Flächenberechnung mit der Gaußschen Trapezformel

The alternative coordinate method computes the area within the traverse using its x and y coordinates, which are arranged sequentially around the shape. 

Each corner's coordinates are written as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator, listed horizontally in order. The first corner's fraction is repeated at the end of the sequence.

Draw solid diagonal lines connecting each x-coordinate to the next y-coordinate in sequence. Similarly, draw dashed diagonal lines connecting each y-coordinate to the next x-coordinate in the same sequence.

Calculate the solid-line contributions by multiplying each x-coordinate with the next y-coordinate.

Similarly, multiply each y-coordinate by the next x-coordinate to compute the dashed-line contributions. 

Twice the area within the traverse is calculated by subtracting the total of the dashed-line products from the total of the solid-line products. 

Take the absolute value of this difference and divide it by two to determine the exact area within the traverse. 

This method is widely used for its simplicity, accuracy, and adaptability for manual and computer-based calculations in surveying.