THE AREA OF A SIMPLE POLYGON

Publisher Summary This chapter presents a formula to calculate the area of a simple polygon. The formula for the area of a triangle is given in “Triangles.” This was generalized by Stone (1986) to a formula for a simple polygon that is easy to remember. The chapter considers P i = ( x i , y i ), i = 1, 2…, n, the counterclockwise enumeration of the vertices of the polygon. The polygon is illustrated in the chapter. The formula for area of the polygon is presented. Meaning of an expression given in the formula is explained. This expression is interpreted as the summing of the products of the “downward” diagonals and subtraction of the product of the “upward” diagonals. A specific example is also presented in the chapter to clarify the formula.