For what type of areas are planar measurements most appropriate?

Planar measurements are most suitable for smaller areas because, within these limited extents, the curvature of the Earth can typically be disregarded, allowing for the use of flat, two-dimensional representations of the geographic space. In such smaller regions, the simplification that comes from assuming a flat surface is adequate for many applications, such as mapping and surveying, where precise distances and angles are necessary.

In contrast, larger areas, like entire continents or hemispherical regions, will exhibit noticeable curvature that can distort measurements if planar methods are applied. Similarly, regions with complex terrain feature uneven elevations and varied topography, which would also complicate the accuracy of planar measurements. Therefore, for accurate representation and analysis, especially when working with geographic data, utilizing planar measurement techniques is best reserved for smaller areas where the effects of Earth's curvature can be ignored.