Equal-area projections are designed to preserve the relative area of landmasses, meaning that the size of regions is represented accurately compared to one another. However, they can exhibit distortions in several ways:
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Directions and Distances: While equal-area projections maintain accurate area relationships, they do not preserve angles or shapes. This means that although the sizes of landmasses are correct, the directions and distances between locations can be distorted.
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Shapes of Landmasses: On an equal-area map, the shapes of landmasses may appear distorted. For instance, areas closer to the poles can be stretched or compressed in a way that makes them look different from their true form.
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Polar Distortion: Areas near the poles can appear disproportionately larger compared to their actual size. This is especially true in projections like the Mollweide or the Peters projection, where polar regions are stretched to maintain equal area.
So, the accurate options regarding the inaccuracies of equal-area projections would focus on distortions of shapes and directions, as well as the representation of areas at extreme latitudes. Therefore, the statement "C directions and the shapes of the landmasses are distorted" is correct, as is "D areas close to the poles are disproportionately large." The first option, regarding the projection not showing true size, is misleading because equal-area projections do show true size relationships, but may distort other attributes.
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