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The volume of a tetrahedron can be obtained in many ways. It can be given by using the formula of the pyramid's volume: =. where is the base' area and is the height from the base to the apex. This applies for each of the four choices of the base, so the distances from the apices to the opposite faces are inversely proportional to the areas of ...
The surface area is the total area of each polyhedra's faces. In the case of a pyramid, its surface area is the sum of the area of triangles and the area of the polygonal base. The volume of a pyramid is the one-third product of the base's area and the height.
A triangular bipyramid with regular faces is numbered as the twelfth Johnson solid . [10] It is an example of a composite polyhedron because it is constructed by attaching two regular tetrahedra. [11] [12] A triangular bipyramid's surface area is six times that of each triangle
An elongated triangular pyramid with edge length has a height, by adding the height of a regular tetrahedron and a triangular prism: [4] (+). Its surface area can be calculated by adding the area of all eight equilateral triangles and three squares: [2] (+), and its volume can be calculated by slicing it into a regular tetrahedron and a prism, adding their volume up: [2]: ((+)).
In geometry, a hyperpyramid is a generalisation of the normal pyramid to n dimensions. In the case of the pyramid one connects all vertices of the base (a polygon in a plane) to a point outside the plane, which is the peak. The pyramid's height is the distance of the peak from the plane. This construction gets generalised to n dimensions.
Therefore, the surface area of a pentagonal pyramid is the sum of the areas of the five triangles and the one pentagon. The volume of every pyramid equals one-third of the area of its base multiplied by its height. So, the volume of a pentagonal pyramid is one-third of the product of the height and a pentagonal pyramid's area. [9]
The surface area of an elongated triangular bipyramid is the sum of all polygonal face's area: six equilateral triangles and three squares. The volume of an elongated triangular bipyramid V {\displaystyle V} can be ascertained by slicing it off into two tetrahedrons and a regular triangular prism and then adding their volume.
The volume is computed as F times the volume of the pyramid whose base is a regular p-gon and whose height is the inradius r. That is, =. The following table lists the various radii of the Platonic solids together with their surface area and volume.