# Difference between revisions of "Convex polygon"

A convex polygon is a polygon whose interior forms a convex set. That is, if any 2 points on the perimeter of the polygon are connected by a line segment, no point on that segment will be outside the polygon.

All internal angles of a convex polygon are less than $180^{\circ}$. These internal angles sum to $180(n-2)$ degrees.

The convex hull of a set of points also turns out to be the convex polygon with some or all of the points as its vertices.

The area of a regular n-gon of side length s is $\frac{ns^2*\tan{(90-\frac{180}{n})}}{4}$

All external angles are less than $180^{\circ}$. These external angles sum to $360$.