Which method is commonly used to accurately determine the area of an irregular boundary on a drawing?

The planimeter is the most effective tool for accurately determining the area of an irregular boundary on a drawing. It is a mechanical device specifically designed for measuring the area of complex shapes, allowing the user to trace the outline of the boundary. As the tracing occurs, the planimeter computes the area directly based on the path followed. This method is particularly useful when dealing with irregular shapes where traditional area calculation formulas may not apply.

In contrast, while CAD software is indeed powerful for various design and drafting tasks, it might not always provide the quickest or most straightforward means of obtaining area measurements for irregular shapes if not specifically configured for that purpose. The triangle method relies on dividing a shape into triangles and summing their areas, which can complicate calculations for irregular boundaries. The grid method involves overlaying a grid onto the shape and counting how many grid squares fall within the area; however, this approach is more approximate and less precise than using a planimeter. Thus, for accuracy in measuring the area of irregular boundaries, the planimeter stands out as the most appropriate choice.