What kind of map is a rectangular representation of earth but she was accurate directions but distorts the sizes and distances

The correct answer is - Mercator projection map.

The Mercator projection map is a cylindrical type of map that represents the Earth in rectangular manner. While the map may seem as a nice representation of the Earth, and it has accurate directions, it also has some flaws. The biggest flaw of this map is the distortion of the sizes. The distortion is non existent on the Equator, but as it moves north and south of it towards the poles, the distortion is constantly increasing. This projection is not made to be able to cope with the increase of the scale, especially when it it is infinite at the poles.

Because of this, on this map, Greenland looks very similar in size with Africa, even though in reality it is around 15 times smaller.