Which method would you use to find the area of land using coordinates?

The area by coordinates method is specifically designed for the task of calculating the area of land parcels using their vertex coordinates. This method employs the coordinate geometry principles, where the x and y coordinates of the corners of the land parcel are utilized to determine the area through a formula, commonly known as the Shoelace formula. This approach is particularly beneficial because it provides an efficient way to calculate areas for irregular shapes without needing to break them down into simpler geometric figures.

In contrast, the other methods mentioned have different applications. The prismoidal method is primarily used in volume calculations for earthwork and not suitable for just determining area. The end area method is utilized for computing volumes, particularly in earthwork projects where cross-sectional areas at different ends are averaged to obtain the volume between them. The measurement method generally refers to direct field measurements, which can be less precise and more labor-intensive compared to the coordinate-based calculations.

Using the area by coordinates method allows for accurate and quicker calculations when the coordinates of the vertices of a parcel are known, making it the most appropriate choice in this scenario.