Parallelepiped vs. Rectangular Prism

Attribute	Parallelepiped	Rectangular Prism
Definition	A three-dimensional figure with six faces, each of which is a parallelogram	A three-dimensional figure with six faces, each of which is a rectangle
Edges	12	12
Vertices	8	8
Diagonals	4	4
Opposite Faces	Parallel and equal in area	Parallel and equal in area

Introduction

Parallelepiped and rectangular prism are two three-dimensional geometric shapes that are often confused due to their similar appearance. While they both have six faces, twelve edges, and eight vertices, there are key differences between the two shapes that set them apart. In this article, we will explore the attributes of parallelepiped and rectangular prism to understand their unique characteristics.

Definition

A parallelepiped is a six-faced figure where each face is a parallelogram. This means that opposite faces of a parallelepiped are parallel and equal in size. On the other hand, a rectangular prism is a six-faced figure where each face is a rectangle. This means that opposite faces of a rectangular prism are parallel and equal in size, with all angles being right angles.

Edges and Vertices

Both parallelepiped and rectangular prism have twelve edges and eight vertices. The edges of a parallelepiped are not necessarily perpendicular to each other, while the edges of a rectangular prism are always perpendicular. This difference in edge orientation affects the overall shape and structure of the two figures. The vertices of a parallelepiped are connected by three edges, while the vertices of a rectangular prism are connected by three edges as well.

Surface Area

The surface area of a parallelepiped is calculated by adding the areas of all six faces. Since the faces of a parallelepiped are parallelograms, the surface area formula involves the base and height of each face. On the other hand, the surface area of a rectangular prism is calculated by adding the areas of all six faces. Since the faces of a rectangular prism are rectangles, the surface area formula involves the length, width, and height of each face.

Volume

The volume of a parallelepiped is calculated by multiplying the base area by the height. Since the base of a parallelepiped is a parallelogram, the volume formula involves the base area and height. On the other hand, the volume of a rectangular prism is calculated by multiplying the length, width, and height. Since the base of a rectangular prism is a rectangle, the volume formula involves the length, width, and height.

Diagonals

The diagonals of a parallelepiped connect opposite vertices that are not connected by an edge. The length of the diagonals can be calculated using the Pythagorean theorem. The diagonals of a rectangular prism connect opposite vertices that are not connected by an edge. The length of the diagonals can also be calculated using the Pythagorean theorem.

Applications

Parallelepipeds are commonly used in engineering and architecture to represent structures such as beams and trusses. The unique shape of a parallelepiped allows for efficient distribution of weight and stress. Rectangular prisms are commonly used in everyday objects such as boxes and containers. The right angles and equal faces of a rectangular prism make it easy to stack and store items.