Perimeters, Areas and Volumes in Geometry

SOLIDS:

Polyhedron:

A polyhedron is a figure formed by four or more noncoplanar polygonal region which enclose a part of space.

polyhedron

-A prism is a polyhedron with two congruent faces contained in parallel planes. All other faces are parallelograms.

prism1

-The lateral edges of a prism are equal and parallel.

-The bases of a prism have equal areas.

-A prism is a right prism  if the lateral edges are perpendicular to the planes of the bases.

-It is an oblique prism if the lateral edges are not perpendicular to the planes of the bases.

-A right prism whose bases are regular polygons is called a regular prism.

-A cube is a regular prism in which all faces are square.

-A parallelepiped is a prism in which all faces are parallelograms

Diagonal of the rectangular solid:

rectangular solid

The diagonal CG:

-The length n of a diagonal of a rectangular solid with length l, width w and height h is :

n=\sqrt{l^{2}+w^{2}+h^{2}}

Areas of a prism:

-The Lateral Area L.A. of a prism is the sum of the areas of its lateral faces. The total area T.A. of a prism is the sum of its lateral area and the areas of its two bases.

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