Final answer:
For accurately displaying one continent, an equal-area projection is best for representing true sizes, while a conic projection can provide a good balance between the size and shape of geographic areas, especially in the temperate zones. The Mercator projection is less suitable as it significantly distorts sizes and shapes at high latitudes.
Step-by-step explanation:
When choosing the best map projection to show one continent, it's important to consider the purpose of the map and the distortion each map type may present. The Mercator projection is a cylindrical map projection where latitude lines are spaced evenly apart, which results in significant distortion of size and shape, especially at high latitudes. It is known for preserving angles and shapes of small regions, making it useful for navigation. However, for accurately representing the size and shape of a continent, a conic projection or an equal-area projection is often more appropriate.
The conic projection is particularly good for showing single continents as it provides a balance between shape and area accuracy. This projection typically has less distortion for temperate zones and the distortion increases further from the central latitude it's optimized for. An equal-area projection, on the other hand, is designed to represent areas correctly, hence the name. This means the relative sizes of different regions on the map are accurate, which is crucial when comparing the geographical sizes of different regions on a continent.
In summary, for a map focusing solely on one continent, the equal-area projection would typically be the most accurate in terms of size representation, while the conic projection can provide a good balance between size and shape, especially for continents located in the temperate zones.