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The volume of a prism is the product of the area of the base by the height, i.e. the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance). The volume is therefore: =, where B is the base area and h is the height.
If two opposite faces become squares, the resulting one may obtain another special case of rectangular prism, known as square rectangular cuboid. [b] They can be represented as the prism graph. [3] [c] In the case that all six faces are squares, the result is a cube. [4]
In geometry, a square pyramid is a pyramid with a square base, having a total of five faces. 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 .
The formula for the volume of a pyramidal square frustum was introduced by the ancient Egyptian mathematics in what is called the Moscow Mathematical Papyrus, written in the 13th dynasty (c. 1850 BC): = (+ +), where a and b are the base and top side lengths, and h is the height.
3D model of a (uniform) heptagonal prism. In geometry , the heptagonal prism is a prism with heptagonal base. This polyhedron has 9 faces (2 bases and 7 sides), 21 edges, and 14 vertices.
The gyroelongated square pyramid is a Johnson solid (specifically, J 10) constructed by augmenting one a square pyramid. Similarly, the gyroelongated square bipyramid (J 17) is a deltahedron (a polyhedron whose faces are all equilateral triangles) constructed by replacing both squares of a square antiprism with a square pyramid.
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]
The dihedral angle of an augmented triangular prism between square and triangle is the dihedral angle of a triangular prism between the base and its lateral face, / = The dihedral angle of an equilateral square pyramid between a triangular face and its base is arctan ( 2 ) ≈ 54.7 ∘ {\textstyle \arctan \left({\sqrt {2}}\right)\approx 54. ...