Final answer:
The Gall-Peters projection sacrifices feature shapes while maintaining accurate sizes. The Mercator projection distorts sizes but preserves shapes. The Robinson projection attempts to balance shape and size accuracy.
Step-by-step explanation:
The type of map projection that sacrifices feature shapes while maintaining more accurate sizes is the Gall-Peters projection. The Gall-Peters projection, also known as the equal-area projection, shows the continents with their accurate sizes but distorts their shapes.
In contrast, the Mercator projection preserves shapes but distorts sizes, especially as latitude increases. It is useful for navigation purposes because it maintains straight lines for constant compass bearings.
The Robinson projection is a compromise projection that attempts to balance both shape and size accuracy, but it still introduces some distortions.
The Conic projection is a projection that preserves neither shape nor size accurately, as it is often used for regional maps with limited areas of coverage.