Prism

Prism, in geometry, three-dimensional solid, of which the bases are two parallel planes. The faces of the prism in these planes are congruent polygons. The lateral faces of the prism are parallelograms (see Fig. 1). The intersections of the lateral faces, called the lateral edges, are parallel to each other. A prism is called a right prism if the lateral edges are perpendicular to the bases; if they are not, it is called an oblique prism. A prism is triangular, square, and so on, according as its bases are triangles, squares, or some other geometrical figure. A parallelepiped is a prism that has parallelograms as the bases; a rectangular parallelepiped, or box, is one in which all six faces (four lateral faces and two bases) are rectangles (see Fig. 2); in a cube the six faces are squares (see Fig. 3).

The altitude of a prism is the perpendicular distance between the planes of the bases. A truncated prism is that portion of a prism between a base and a section formed by a plane not parallel to the base but cutting all lateral edges (see Fig. 4). The volume, V, of a prism is given by the area, B, of a base multiplied by the altitude, h; in symbols, V = Bh. If a,b,c are the lengths of three edges of a rectangular parallelepiped that meet at one vertex (the length, width, and depth of a box), the volume is given by V = abc. In particular, if a is the length of one of the twelve equal edges of a cube, the volume of the cube is V = a³ and the total surface area, S, of the cube is S = 6a².

See also Cylinder; Geometry; Solid Geometry.