The formula for calculating the polygon area is1/2 * n * sin (2π/n) * r 2. A plane figure composed of three or more line segments connected end to end is called a polygon. According to different standards, polygons can be divided into regular polygons and irregular polygons, convex polygons and concave polygons.

There are at least three line segments that make up a polygon, and a triangle is the simplest polygon. Each line segment that constitutes a polygon is called an edge of the polygon; The common endpoint of two adjacent line segments is called the vertex of the polygon; The angle formed by two adjacent sides of a polygon is called the inner angle of the polygon; The line segment connecting two nonadjacent vertices of a polygon is called the diagonal of the polygon.

Knowledge expansion

In mathematics, a closed figure consisting of three or more line segments connected end to end is called a polygon. According to different standards, polygons can be divided into regular polygons and non-regular polygons, convex polygons and concave polygons (geometric elements are defined as four sides or more).

A finite number of points A 1, A2, A3, …, An- 1, a and line segments A 1, A2, A2A3, …, An- 1A are called polylines. A 1 and a are called the endpoints of this polyline; A2, A3, …, An- 1 are called vertices of polylines; A 1A2, A2A3, …, An- 1A2 are called polylines. If the endpoints and vertices of a polyline are not on the same plane, it is called a spatial polyline. If each vertex and both ends are on the same plane, it is called a planar polyline.

A broken line whose two ends coincide is called a polygon. Polygons composed of spatial polylines are called spatial polygons; A polygon composed of planar polylines is called a planar polygon. If both ends of the dotted line A 1A2A3…An- 1A coincide with A, a polygon A1A3a3 … an-1a is formed; A 1A2, A2A3, …, An- 1A2 are called polygons;

∠A 1A2, ∠ A 1A3a3, … are called the angles of a polygon; A 1, A2, A3, …, An- 1, a is called the vertex of this polygon. Plane polygons can be divided into three sides (angles), quadrangles, pentagons and hexagons according to the number of sides.