Chapter II

                                                     Methodology         

          if all sides and angles of a polyhedron are equal, it is called a regular polyhedron. The Intraoctagon formed in this mathematical investifatory project is a regular polyhedron. Having its equal sides, the volume of Intraoctagon was determined.

            The Octagonaal prism’s face was drawn on a cartesian plane. The vertices and medians were assigned by using the pythagorean theorem, which states that a triangle with an internal angles of 45-45-90 have 1 in its 2 adjacent sides of 90 and  in its hypothenus. Each side was assigned as 2a. The vertices were connected to the medians opposing it. The connected vertices to medians were called exclusive medians. The slopes of the exclusive medians were computed to determine the equation of the lines. After getting the slopes of the exclusive medians, the line equations were obtained using the slope and point in point slope formula. After getting the equation of the lines, ellimination method was used to determine the intersections or the new vertices for the intraoctagon. The distance formula was used to prove that the distances  of the vertices formed inside were equal. the method of ratio and proportion was used to get the volume of the intraoctagon to the volume of the regular octagonal prism. The derived formula for the intraoctagon was obtained by deriving the formula of the regular octagon’s volume by using the side of the new intraoctagon.