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The surface area of a cube is six times the area of a square: [4] =. The volume of a cuboid is the product of its length, width, and height. Because all the edges of a cube are equal in length, it is: [ 4 ] V = a 3 . {\displaystyle V=a^{3}.}
b = the base side of the prism's triangular base, h = the height of the prism's triangular base L = the length of the prism see above for general triangular base Isosceles triangular prism: b = the base side of the prism's triangular base, h = the height of the prism's triangular base
If its three perpendicular edges are of unit length, its remaining edges are two of length √ 2 and one of length √ 3, so all its edges are edges or diagonals of the cube. The cube can be dissected into six such 3-orthoschemes four different ways, with all six surrounding the same √ 3 cube diagonal.
An oblique prism is a prism in which the joining edges and faces are not perpendicular to the base faces. Example: a parallelepiped is an oblique prism whose base is a parallelogram, or equivalently a polyhedron with six parallelogram faces. Right Prism. A right prism is a prism in which the joining edges and faces are perpendicular to the base ...
The parts of the unit cube that remain, after emptying this hole, form two triangular prisms and two irregular tetrahedra, connected by thin bridges at the four vertices of the square. Each prism has as its six vertices two adjacent vertices of the cube, and four points along the edges of the cube at distance 1/4 from these cube vertices.
Any of the three pairs of parallel faces can be viewed as the base planes of the prism. A parallelepiped has three sets of four parallel edges; the edges within each set are of equal length. Parallelepipeds result from linear transformations of a cube (for the non-degenerate cases: the bijective linear transformations).
Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
The area of a triangle is proportional to the excess of its angle sum over 180°. Two triangles with the same angle sum are equal in area. There is an upper bound for the area of triangles. The composition (product) of two reflections-across-a-great-circle may be considered as a rotation about either of the points of intersection of their axes.