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.
Regular polygons
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
Simple polygons have sides that do not intersect or cross each other:
Complex polygons
Complex polygons have sides that intersect:
Convex polygons
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”.
Concave polygons
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.