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Rectangular Solid Geometry Formula

In a rectangular solid all angles are right angles and opposite faces of an equal cuboid. It is also a right rectangular prism. The term rectangular or oblong prism is ambiguous. It is also referred to by the term rectangular parallelepiped or orthogonal parallelepiped.

The square cuboid, square box, or right square prism also ambiguously called square prism is a special case of the cuboid in which at least two faces are squares. The cube is a special case of the square cuboid in which all six faces are squares.

If the dimensions of a cuboid are a, b and c, then its volume is abc and its surface area is 2ab + 2bc + 2ac. The length of the space diagonal is -

d = \sqrt{a^2+b^2+c^2}.\

Cuboid shapes are often used for boxes, cupboards, rooms, buildings, etc. Cuboids are among those solids that can tessellate 3-dimensional space. The shape is fairly versatile in being able to contain multiple smaller cuboids, e.g. sugar cubes in a box, small boxes in a large box, a cupboard in a room, and rooms in a building.

A cuboid with integer edges as well as integer face diagonals is called an Euler brick. A perfect cuboid is a Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists.

rectangular solid

Volume of rectangular solid = lwh

Surface area of rectangular solid = 2(lw + wh + lh)
 
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