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A polyhedron's surface area is the sum of the areas of its faces. 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.
A pyramid is a polyhedron that may be formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form an isosceles triangle, called a lateral face. [7] The edges connected from the polygonal base's vertices to the apex are called lateral edges. [8] Historically, the definition of a pyramid has been described by ...
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
Frustum. In geometry, a frustum ( Latin for 'morsel'); [ a] ( pl.: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. A right frustum is a right pyramid or a right cone ...
Prism (geometry) In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases.
An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle ), so that the height of the ...
The surface area of a regular octahedron can be ascertained by summing all of its eight equilateral triangles, whereas its volume is twice the volume of a square pyramid; if the edge length is , [4] =, =. The radius of a circumscribed sphere (one that touches the octahedron at all vertices), the radius of an inscribed sphere (one that tangent ...
In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular hexagons and 6 squares ), 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a 6 ...
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