What is the shape of the shoe boxes, books, and bricks called? Is it a rectangle or a parallelogram? It is a Rectangular Parallelepiped. Let us understand what a parallelepiped is. A Parallelepiped is a 3D shape made up of six parallelograms. A rectangular parallelepiped is a kind of parallelepiped made up of rectangular-shaped parallelograms. All the opposite faces of the rectangular parallelepiped are equal and parallel, and the parallel edges are of the same length. This article deals with the definition of Rectangular Parallelepiped, characteristics of Rectangular Parallelepiped, and Rectangular Parallelepiped Formula.

What is a Parallelepiped? 

A Parallelepiped is made up of six parallelograms. It is a 3D shape. The word parallelepiped traces its origin back to the parallelepipdon, a Greek word meaning a body that has parallel bodies. A Parallelepiped consists of 6 parallelogram look-alike faces, 12 edges, and eight vertices. Some special kinds of parallelepiped are cube, rhombus, and cuboid.  

What is the definition of Rectangular Parallelepiped?

A rectangular parallelepiped, better known as cuboid, is a parallelepiped with rectangular faces. Therefore a rectangular parallelepiped can be defined as a 3D shape that is made up of six rectangular-shaped parallelograms. Hence, it comprises six faces wherein all the opposite faces are parallel and equal. It is also a hexahedron, a polyhedron consisting of six faces. Some common examples of rectangular parallelepiped are a shoebox, bricks, books, carton boxes, etc.

What are the characteristics of Rectangular Parallelepiped?

The characteristics of Rectangular Parallelepiped are as follows –

1. A rectangular parallelepiped is a 3D shape. 
2. It is made up of six rectangular-shaped parallelograms. 
3. It is also known as a cuboid.
4. All the opposite faces are equal and parallel. 
5. The parallel edges are of the same length. 
6. The diagonal which goes along each face is known as the face diagonal.
7. Three faces of the Rectangular Parallelepiped are visible at the same time.
8. It is a hexahedron, which signifies a polyhedron consisting of six faces.

What are Rectangular Parallelepiped Formulas?

A rectangular parallelepiped is a three-dimensional figure. The three dimensions are length, height, and breadth, further denoted as l,h, and b, respectively. The Rectangular Parallelepiped Formulas which are used to calculate its lateral surface area, surface area, diagonal, and volume are as follows-

Consider a shoebox, and there are six faces of the shoe box. Let’s say A and B are two opposite side faces, C and D are two other opposite side faces, and E and F are top and bottom faces.

• Total surface Area or TSA-

The total surface area of a rectangular parallelepiped is the surface area of all its faces. It means it is the total area of six rectangular faces. 

Therefore, the Total surface area of the Rectangular Parallelepiped = 2 × area of A + 2 × area of C + 2 × area of D.

 ( As B, D and F are equal to A, C, and E)

                  TSA = 2× area of parallelogram + 2 × area of parallelogram C + 2 × area of parallelogram.       

                  TSA = 2× L × B + 2 × B × H+ 2 × H × L.

                  TSA = 2( LB + BH + HL).

• Lateral surface area or LSA-

The lateral surface area of the rectangular parallelepiped means the area of all the sides of the rectangular parallelepiped. It is the product of the height and Perimeter of the base. 

The lateral surface area of rectangular parallelepiped = Perimeter of the Base × height.

( As the base of a rectangular Parallelepiped is a rectangle. Therefore its Perimeter will be equal to that of a rectangle)

                   LSA = 2 (length + breadth) × height. 

                   LSA = 2 ( lh+ bh).

Also, the total surface area can be calculated as 

        TSA = LSA + 2LW.

• Volume or V-

The volume of the rectangular parallelepiped refers to the space occupied by the rectangular parallelepiped. It is the product of the area of the face and the height of the rectangular parallelepiped.

The volume of Rectangular Parallelepiped = Area of the Base × height.

( As the base of a rectangular Parallelepiped is a rectangle. Therefore its volume will be equal to that of a rectangle)

                    V = L× b × h.

                    V = LBH

• Diagonal formula –

A diagonal in a rectangular Parallelepiped can be defined as a straight line that connects two opposite corners of a rectangular Parallelepiped by its vertex.

The length of the Diagonal in a Rectangular Parallelepiped = √ l2 + b2 + h2 

Conclusion 

A definition of Rectangular Parallelepiped is a 3D shape that is made up of six rectangular-shaped parallelograms. It is a special kind of parallelepiped with all rectangular-shaped parallelograms. It is commonly known as a cuboid. It is a polyhedron with six rectangular faces, known as hexahedra. Shoeboxes, books, and bricks are some examples of a rectangular parallelepiped. The main characteristics of a rectangular parallelepiped are that all the opposite faces of the rectangular parallelepiped are equal and parallel, and The parallel edges are of the same length.