How do polygons relate to the real world?
Igloos, Cones (such as ice cream cone), triangles (such as roofs seen from one side only), groundwater plumes (perfectly shaped if below ground conditions are homogeneous and isotropic) are some examples.
Any form of tiling involves polygons. The tiles need to tessellate to cover an area without leaving any gaps. This is directly connected to the angle properties of polygons.
Architects include polygons with every plan of a house - rooms usually have 90° corners, but not always. Rooms on a plan are polygons.
The cost of building any structure depends on the lengths of the walls and the size of the angles - all properties of polygons.
If a single free-standing room is to be built, the greatest ratio between the area and the perimeter is in a circle.
The smallest ratio between the area and the perimeter is found in a triangle. The best ratio in tessellating polygons is in a hexagon.
As soon as the cost of doing something one way as compared to another, it becomes a real life issue.
We are surrounded by polygons all the time.