Which of the following types of maps shows correct shapes and directions but distorts distances sizes.

equal area projection
mercator projection
mollweide projection
robinson projection

- Mercator projection

The correct answer is the Mercator projection. The Mercator projection is a cylindrical map projection that preserves accurate shapes and directions but distorts distances and sizes, particularly at high latitudes.

The type of map that shows correct shapes and directions but distorts distances and sizes is the Mercator projection.

To understand why this is the case, let's first look at what a Mercator projection is. The Mercator projection is a cylindrical map projection developed by Gerardus Mercator in the 16th century. It became widely used for navigation purposes because it accurately preserved angles and shapes, making it useful for sailors to plot a straight course on a constant bearing.

However, the downside of the Mercator projection is that it distorts the size of objects as you move away from the equator. This means that areas near the poles appear significantly larger than they actually are. The distortion occurs because the Mercator projection stretches out the areas closer to the poles to fit the rectangular shape of the map, resulting in an exaggerated representation of the true size of those areas.

Additionally, the Mercator projection also distorts distances. As you move toward the poles, the scale of the map increases, causing distances to appear larger than they actually are. For example, Greenland appears much larger on a Mercator projection map compared to its actual size.

In contrast, let's briefly explain the other map projections you mentioned:

1. Equal area projection: This type of map projection, also known as an equal-area map, attempts to preserve accurate relative sizes of all areas on the map. While it maintains accurate representation of sizes, it may distort shapes or angles.

2. Mollweide projection: The Mollweide projection is an equal-area projection that attempts to show accurate sizes and shapes of land masses. However, it does distort directions and distances, particularly towards the edges of the map.

3. Robinson projection: The Robinson projection is a compromise projection that attempts to balance the distortion of shapes, sizes, and distances across the entire map. It does not preserve any one attribute perfectly, but it provides a visually pleasing representation of the whole world.

In summary, while the Mercator projection accurately shows shapes and directions, it distorts distances and sizes, especially in areas closer to the poles. This is why the Mercator projection is commonly criticized and alternative map projections, such as the equal area, Mollweide, and Robinson, have been developed to address these distortions.