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In geometry, a square pyramid is a pyramid with a square base and four triangles, 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.
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
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. Given that is the base's area and is the height of a pyramid, the volume of a pyramid is: [29] =.
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.
This gives the expected results of 4 π steradians for the 3D sphere bounded by a surface of area 4πr 2 and 2 π radians for the 2D circle bounded by a circumference of length 2πr. It also gives the slightly less obvious 2 for the 1D case, in which the origin-centered 1D "sphere" is the interval [−r, r] and this is bounded by two limiting ...
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 volume (V) and surface area (S) of a toroid are given by the following equations, where r is the radius of the circular section, and R is the radius of the overall shape. V = 2 π 2 r 2 R {\displaystyle V=2\pi ^{2}r^{2}R}
Calculation of the area of a square whose length and width are 1 metre would be: 1 metre × 1 metre = 1 m 2. and so, a rectangle with different sides (say length of 3 metres and width of 2 metres) would have an area in square units that can be calculated as: 3 metres × 2 metres = 6 m 2. This is equivalent to 6 million square millimetres.