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An augmented triangular prism with edge length has a surface area, calculated by adding six equilateral triangles and two squares' area: [2] +. Its volume can be obtained by slicing it into a regular triangular prism and an equilateral square pyramid, and adding their volume subsequently: [ 2 ] 2 2 + 3 3 12 a 3 ≈ 0.669 a 3 . {\displaystyle ...
The surface area of a right square pyramid can be expressed as = +, where and are the areas of one of its triangles and its base, respectively. The area of a triangle is half of the product of its base and side, with the area of a square being the length of the side squared.
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]: ((+)).
Its surface area can be calculated by adding all the area of four equilateral triangles and four squares: [3] (+). Its volume is obtained by slicing it into an equilateral square pyramid and a cube, and then adding them: [ 3 ] ( 1 + 2 6 ) a 3 ≈ 1.236 a 3 . {\displaystyle \left(1+{\frac {\sqrt {2}}{6}}\right)a^{3}\approx 1.236a^{3}.}
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. The pyramid height is defined as the length of the line segment between the apex and its orthogonal projection on the base.
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A normal triangle is a 2-dimensional hyperpyramid, the triangular pyramid is a 3-dimensional hyperpyramid and the pentachoron or tetrahedral pyramid is a 4-dimensional hyperpyramid with a tetrahedron as base. The n-dimensional volume of a n-dimensional hyperpyramid can be computed as follows: = Here V n denotes the n-dimensional volume of the ...
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