Remarks on the Surface Area and Equality Conditions in Regular Forms. Part I: Triangular Prisms

This work presents four mathematical remarks concluded from the mathematical analysis for the interrelationships between the dependent and independent variables that control the measures: perimeter, floor area, walls surface area and total surface area in the regular forms that have a given volume. Such forms include prismatic and pyramidal forms. The work consists of four parts, of which this first part presents the remarks of the isosceles triangular right prism. The first remark examines the effect of θ, the angle of the triangular base, on the total surface area. The second remark calculates the minimum total surface area in two cases, depending on whether angle θ is constant or variable. The third remark calculates the walls ratio and the critical walls ratio. The last remark studies the required conditions for the numerical equality in two cases, where the perimeter is equal to the area, and where the total surface area is equal to the volume.