Name a map projection that preserves area and one that preserves shape, and describe a typical trade-off.

Name a map projection that preserves area and one that preserves shape, and describe a typical trade-off.

• A. Mercator projection preserves area and Peters preserves shape; trade-offs include distortion in distance.
• B. Mercator projection preserves shape and Peters preserves area; trade-offs include distortion in distance and size.
• C. Peters (area-preserving) and Mercator (shape-preserving); trade-offs include distortion in other properties.
• D. Lambert conformal projection preserves area and equal-area projection preserves shape; trade-offs include distortion in longitude.

Answer: (C)

Maps that must flatten a curved surface inevitably lose something in the process. You can pick to keep area sizes accurate (area-preserving) or to keep shapes accurate (shape-preserving), but not both everywhere on the map. Peters is an equal-area projection, so it preserves the relative sizes of lands—continents look proportional to their true areas—even though their shapes become distorted compared with reality. Mercator is a conformal projection, which preserves angles and local shapes, so small regions look right in shape, and navigation is easier because lines of constant bearing plot as straight lines, but its area and size distortions grow with distance from the equator. The combination described in the correct choice—Peters preserving area and Mercator preserving shape—best illustrates this trade-off, with the caveat that other properties such as distance or overall area accuracy will be distorted. The other options mix up which projection preserves area or shape, so they don’t reflect the actual trade-offs.

Maps that must flatten a curved surface inevitably lose something in the process. You can pick to keep area sizes accurate (area-preserving) or to keep shapes accurate (shape-preserving), but not both everywhere on the map. Peters is an equal-area projection, so it preserves the relative sizes of lands—continents look proportional to their true areas—even though their shapes become distorted compared with reality. Mercator is a conformal projection, which preserves angles and local shapes, so small regions look right in shape, and navigation is easier because lines of constant bearing plot as straight lines, but its area and size distortions grow with distance from the equator. The combination described in the correct choice—Peters preserving area and Mercator preserving shape—best illustrates this trade-off, with the caveat that other properties such as distance or overall area accuracy will be distorted. The other options mix up which projection preserves area or shape, so they don’t reflect the actual trade-offs.