Triangular Units Theorem for Areas of Regular Polygons

Teresa J. Sanchez, Kharisse Grace J. Sanchez

Abstract: This paper provides a step-by step derivation of a new formula for finding the area of a regular polygon of any side n inscribed in a circle of radius r in terms of triangular units. It introduces the term triangular units and its corresponding formula. Based on the formula for the area of a regular polygon of side n, u2 the researchers derived the formula for the area of a regular polygon of side n terms of triangular units. An = n r2 ? u, where ? u = ? sin 360?/n This new formula is called Triangular Units Theorem for Areas of Regular Polygon.

Keywords: polygon, regular polygon, triangular sector of a regular n-gon, triangular unit of a regular n-gon, area of a regular polygon