# Cuboid

A cuboid is a space shape with six rectangular faces. Its angles are all right angles and its opposite faces are equal and parallel to each other.

If all the faces of a cuboid are square, it is usually known as a cube. If the bases of a cuboid are square, it is also called a square prism.

A cuboid is one of the most common shapes in everyday life. A box, a refrigerator, and a book are all cuboids.

## Characteristics of a cuboid

The six faces of a cuboid are often categorized as four lateral faces and two bases. An edge of a cube is a line segment formed by the intersection of two adjacent faces. A vertex of a cube is the point of intersection of three edges.

A cuboid has the following characteristics:

• A cuboid has 6 faces, 12 edges, and 8 vertices.
• The 6 faces of a cuboid are all rectangles. The opposite faces are congruent and in parallel planes. Any two adjacent bases are in perpendicular planes.
• The 12 edges of a cuboid are in 3 groups of parallel lines. The parallel edges are equal in length. Any intersecting edges are perpendicular to each other.

A cuboid is a special type of rectangular prism. To be classified as a cuboid, the lateral faces of the figure must be perpendicular to its bases. In a rectangular prism, the lateral faces do not have to be perpendicular to its bases, as shown in the figure below.

## Surface area of a cuboid

The total surface area, S, of a cuboid is

S = 2·(l·w + w·h + l·h)

where l is the length, w is the width, and h is the height of the cuboid. The height of a cuboid is the length of one of its edges that is perpendicular to the bases. The length and width are adjacent edges of one of the bases as shown below. Usually, the longer length of the base is considered the length, while the shorter length is considered the width.

## Volume of a cuboid

The volume, V, of a cuboid is

V = l·w·h

where l is the length, w is the width, and h is the height of the cuboid.