Cuboid

A cuboid is a three-dimensional solid object bounded by six faces that are rectangles. It is a special type of prism whose bases are rectangles, and also a special type of parallelepiped where all the angles are right angles. Equivalently, it is a rectangular hexahedron.

A cuboid is fully defined by its length (l), width (w), and height (h). These three dimensions are mutually perpendicular.

Special cases of cuboids include:

• Cube: A cuboid where all sides are of equal length (l = w = h).

• Square Prism: A cuboid where at least two faces are squares (l = w, or w = h, or l = h).

Key properties of a cuboid:

• Faces: 6 rectangular faces.
• Edges: 12 edges.
• Vertices: 8 vertices (corners).
• Diagonals: Four space diagonals, all of equal length.

Formulas related to a cuboid:

• Surface Area (A): A = 2(lw + lh + wh)
• Volume (V): V = lwh
• Space Diagonal (d): d = √(l² + w² + h²)

Cuboids are prevalent in everyday life and are commonly found in objects such as boxes, buildings, and rooms. They are fundamental geometric shapes with straightforward properties and calculations, making them important in various fields including architecture, engineering, and computer graphics.