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The surface area of a regular tetrahedron is four times the area of an equilateral triangle: [6] = =. The height of a regular tetrahedron is 6 3 a {\textstyle {\frac {\sqrt {6}}{3}}a} . [ 7 ] The volume of a regular tetrahedron can be ascertained similarly as the other pyramids, one-third of the base and its height.
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
The Egyptians knew the correct formula for the volume of such a truncated square pyramid, but no proof of this equation is given in the Moscow papyrus. The volume of a conical or pyramidal frustum is the volume of the solid before slicing its "apex" off, minus the volume of this "apex":
Given the edge length .The surface area of a truncated tetrahedron is the sum of 4 regular hexagons and 4 equilateral triangles' area, and its volume is: [2] =, =.. The dihedral angle of a truncated tetrahedron between triangle-to-hexagon is approximately 109.47°, and that between adjacent hexagonal faces is approximately 70.53°.
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]: ((+)).
The surface area of a polyhedron is the sum of areas of its faces, for definitions of polyhedra for which the area of a face is well-defined. The geodesic distance between any two points on the surface of a polyhedron measures the length of the shortest curve that connects the two points, remaining within the surface.
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.