Philippine E-Journals

Verifying Volumes and Dimensions of Platonic Solids and their Duals: Basis for Enhanced Learning Plan in Mathematics

Christine D Alagasi | Renan P. Limjuco | Daniel R Aguinaldo

 

Abstract:

Solving volumes and dimensions of Platonic solids aka regular convex polyhedra may be daunting to students; thus, inclusion of these special polyhedra in teaching math has remained an untaken challenge to many teachers. This study verified the volumes and dimensions of the Platonic solids (tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron) and their duals by experiential and computational techniques, and determined existence of significant differences between the experiential-derived and computational-derived volumes. This study employed descriptive comparative research design, purposive selection of two Grade 8 classes from two secondary schools, and descriptive mean and t test to analyze the data. Overall, the descriptive results revealed variations in the obtained mean volumes using experiential approach but only very minimal variation in the mean volumes obtained by computational technique. Further, paired t test revealed no significant difference in tetrahedron’s mean volume taken by computational and experiential methods. However, significant differences existed in the other four Platonic solids’ mean volumes obtained using the two different approaches. Moreover, this study accomplished derivation of formulae for the calculation of the edge of the polyhedra duals, hence also their volumes. The results revealed that the tetrahedron-tetrahedron self-dual demonstrated the highest volume ratio. Based on the findings, an enhanced learning plan in Geometry integrating the use of Platonic solids as learning manipulative was developed.