Difference between Mercator and the Peters Projection Map

Today in class, we talked about the difference between the Peters Projection Map and the Mercator Map. The Peters Projection Map is useful because it has the correct size of each continent and country unlike the Mercator. On the Mercator map, the size of the continents and countries are inaccurate; Greenland looks like it's about the same size as North America when in reality, it's much smaller. Africa looks so much smaller on the map when it is actually bigger than Europe. The Peters Projection Map can give you an accurate shape and size of the continents. However, though they make the size and shape accurate, they also stretch countries and continents near the poles to an inaccurate location.

The Mercator Map is useful because they give you an accurate destination with longitude and latitude unlike the Peters Projection Map. On the Peters Map, they don't give you an accurate location. The Mercator Map is useful for sailors mainly because they give you an accurate direction for small areas.
However, the Mercator Map doesn't give you the correct size and shape of the continent and the countries. Both maps have their pros and cons. I believe that they should both be used. The Mercator Map should be used if you're only looking at the United States, and the Peters Map should be used for the world.
                                                                         Mercator Map:                                                 
 
Peters Projection Map: