Question

why does a mercator projection exaggerate the areas of landmasses near the poles?

Explanation:

The Mercator projection is a cylindrical map projection. To preserve angles (for navigation, as it's a conformal projection), the scale factor (ratio of map distance to Earth - surface distance) increases with latitude. Near the poles, as latitude approaches 90°, the secant of latitude ($\sec(\phi)$) used in its formula ($x = R\phi$, $y = R\ln(\tan(\frac{\pi}{4}+\frac{\phi}{2}))$ for a sphere of radius $R$) becomes very large. This means that the distance on the map between lines of latitude increases rapidly at high latitudes. Since area distortion is related to the square of the scale factor (for conformal projections, area scale factor is the square of the linear scale factor), the areas of landmasses near the poles, which are at high latitudes, get exaggerated because the linear scale is stretched more and more as we move towards the poles.

Answer:

The Mercator projection is conformal (preserves angles) but distorts area. Its formula uses a scale factor related to $\sec(\text{latitude})$, which increases sharply near the poles. As latitude approaches 90° (poles), the linear scale (map - to - Earth distance ratio) grows, and since area distortion is the square of the linear scale factor, landmasses near the poles (high - latitude regions) have their areas exaggerated.