AREA OF PLANAR POLYGONS AND VOLUME OF POLYHEDRA

Publisher Summary This chapter discusses formulas for calculating area of planar polygons and volume of polyhedra. It considers a planar polygon with vertices P 0 ,…, P n . There is a simple closed formula for the area of the polygon. If P n +1 = P 0 and if the points P 0 ,……, P n lie in the xy plane, then the formula for area of polygon can be derived from Green's theorem. If the points lie on some arbitrary plane perpendicular to a unit vector N , then the formula for area of the polygon is derived from Stokes theorem. These two formulas are valid even for nonconvex polygons. The chapter discusses formula for volume of a Polyhedron. It consider a polyhedron with planar polygonal faces S 0 ,…, S n . The chapter highlights that there is a simple closed formula for the volume of the polyhedron which is derived from Gauss Theorem.