A polygon is a two-dimensional (flat) shape created by connecting a number of straight lines. Circles and ellipses are not polygons, because they are made of curved, not straight, lines.
Polygons are named according to the number of sides they have – the number of straight-line segments that are used in drawing the polygon: Three sides- triangle, four sides- quadrangle, etc.
If all the sides of a polygon are of equal length, and all its angles have the same measure, we call that polygon ‘regular’.
Simple polygons have sides that do not intersect or cross each other:
Complex polygons have sides that intersect:
Simple polygons where any two points on their sides (the perimeter) can be connected with a line that does not go outside the polygon are called “convex”.
Polygons, where two points on the perimeter can be connected with a line that goes outside the polygon, are called concave.
Our focus: simple convex polygons
With a few exceptions, we will only concern ourselves with simple convex polygons. It is rare to see high school geometry problems that involve concave polygons or self-intersecting polygons. And those that do, typically have answers that involve treating those complex polygons as a number of simple polygons side by side.