What principle helps in determining areas of irregular shapes in surveying?

The area formulation principle is essential for determining areas of irregular shapes in surveying. This principle outlines various methods and formulas specifically designed to calculate the area of polygons and other complex shapes that cannot be easily measured using standard geometric formulas. One common application of this principle involves dividing the irregular shape into smaller, regular shapes (like triangles or rectangles) for which the area can be easily calculated, and then summing those areas to obtain the total area.

In comparing this principle to the others in the choices, the Pythagorean theorem relates to the relationship between the sides of right triangles and is less applicable for area calculation in irregular shapes. The law of cosines, while useful for finding sides or angles in triangles, does not directly address area calculation for complex shapes. The method of sections is more relevant to structural analysis and the determination of forces in statics rather than the direct calculation of area. Therefore, the area formulation principle stands out as the most relevant and effective choice for this specific task in surveying.