Regular polygon; Let the radius of a regular N-polygon be R, the side length be an, the central angle be αn, and the vertex be R..

N, then α n = 360 ÷ n, an = 2RSin (180 ÷ n), r

n=Rcos( 180 ÷n),R^2=r

N 2+(an ÷ 2) 2, perimeter pn=n×an, area Sn=pn×rn÷2.

If it is not a regular polygon, divide the polygon into several triangles and sum them. Specific analysis of specific problems.