A lambert quadrilateral is a special type of shape that is used for map projections. Imagine you have a round globe and you want to make a flat map of it. The problem is that the round globe is curved and the flat map is, well, flat. So, to make a map, you need to "flatten" the curve of the globe.
A lambert quadrilateral is a shape that helps to "stretch out" areas on a map so that they look more like they do on the globe. It's like taking a piece of paper and cutting it into a special shape that you can use to wrap around the globe, then using that same shape to make a map.
In the lambert quadrilateral, the sides of the shape are curved, which helps to maintain the correct distances between locations on the map. Also, one of the sides is straight, which makes it easier to measure distances and angles.
So, to summarize, a lambert quadrilateral is a special shape used for map projections that helps to stretch out areas on a map so they look more like they do on the globe, while maintaining correct distances and angles.