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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.
Given that is the base's area and is the height of a pyramid, the volume of a pyramid is: [25] =. The volume of a pyramid was recorded back in ancient Egypt, where they calculated the volume of a square frustum, suggesting they acquainted the volume of a square pyramid. [26]
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]: ((+)).
Geometric representation of the square pyramidal number 1 + 4 + 9 + 16 = 30. A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. [1] The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of sides. [2]
If the apex of the pyramid is directly above the center of the square, it is a right square pyramid with four isosceles triangles; otherwise, it is an oblique square pyramid. When all of the pyramid's edges are equal in length, its triangles are all equilateral. It is called an equilateral square pyramid, an example of a Johnson solid.
The surface area of a gyroelongated square bipyramid is 16 times the area of an equilateral triangle, that is: [4], and the volume of a gyroelongated square bipyramid is obtained by slicing it into two equilateral square pyramids and one square antiprism, and then adding their volume: [4] + +.
In geometry, the elongated pyramids are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal prism. Along with the set of pyramids, these figures are topologically self-dual. There are three elongated pyramids that are Johnson solids: Elongated triangular pyramid (J 7), Elongated square pyramid (J 8), and
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.