## Arbitrary Polygons

At first you have to enter the coordinates of the vertices of the polygon.

Then the area, the circumference and the coordinates of the centroid are displayed and the polygon is plotted.

The sides and angles of the polygon are also calculated and it is checked whether the polygon is convex, concave or self-intersecting.

Convex polygon:

Concave polygon:

Self-intersecting polygon:

In addition, convex polygons are checked whether they have an incircle and/or a circumcircle.

Tangent polygon:

Cyclic polygon:

### Example:

Vertices: Area A = 18 A(0|0) B(4|1) Perimeter p = 22,032567 C(6|0) D(5|7) Centroid of vertices: CV(3,75|2) Centroid of area: CA(3,72222|2,66667) Sides: Angles: |AB| = 4,1231056 ∡BAD = 36,158185° |BC| = 2,236068 ∡CBA = 220,60129° |CD| = 6,0827625 ∡DCB = 53,972627° |DA| = 7,8102497 ∡ADC = 49,267893° Concave polygon

∡BAD is the angle by which the ray [AB[

is rotated counterclockwise to [AD[.