 # Rectangular Prism

In Mathematics, Geometry is the study of shapes and configuration of objects. A rectangular prism is the same as a cuboid. A rectangular prism is a polyhedron with two congruent and parallel bases. In this article, let us discuss the definition, types, surface area, and volume of a rectangular prism in detail.

## Rectangular Prism Definition

A rectangular prism is a three-dimensional shape. It has six faces, and all the faces of the prism are rectangles. Both the bases of a rectangular prism must be a rectangle. Also, the other lateral faces will be rectangles. It is also called a cuboid. ## Types of Rectangular Prism

Rectangular prism can be classified into two different types. They are:

### Right Rectangular Prism

A prism with rectangular bases is called a rectangular prism. A right rectangular prism is a prism which has six faces that are rectangles, and all angles are right angles.

• Vertices of a rectangular prism = 8
• Edges of a rectangular prism = 12
• Faces of a rectangular prism= 6 (including bases)

### Oblique Rectangular prism

An oblique prism is a prism in which the bases are not perpendicular to each other. A rectangular prism with bases that are not aligned one directly above the other is an oblique rectangular prism.

## Rectangular prism Formulas

Let ‘l’, ‘w’ and ‘h’ be the length, width and height of the rectangular prism. The formulas are given below.

### Volume of a Rectangular Prism Formula

The volume of a rectangular prism is a measurement of the occupied units of a rectangular prism. The volume of a rectangular prism is represented by cubic units. It is also defined as the number of units used to fill a rectangular prism.

The volume of the rectangular prism is equal to the area of the base times its height.

Therefore, the volume of a rectangular prism formula is given as

The volume of a rectangular prism = Length x Width x Height cubic units.

Volume = l x w x h cubic units

### Lateral Surface Area of a Rectangular Prism

The lateral surface area of a rectangular prism is the sum of the surface area of all its faces without the base of the rectangular prism. The lateral surface area of any right rectangular prism is equivalent to the perimeter of the base times the height of the prism.

Therefore, the lateral surface = PH

Where

P is the perimeter of a base

h be the height of the prism

The perimeter of the rectangular prism is,

P = 2 (l + w)

Therefore, the lateral surface area of a rectangular prism = 2 ( l + w ) h square units.

### Surface Area of a Rectangular Prism

The surface area of a rectangular prism is the measure of how much exposed area a prism has. Surface area is expressed in square units. The surface area of a rectangular prism is the sum of the lateral surface area and twice the base area of the rectangular prism.

Surface Area, (SA) = Lateral Surface Area + 2 (Base Area)

Therefore, the surface area of a rectangular prism formula is given as,

Area of a rectangular prism = 2 (lh +wh + lw ) Square units.

### Rectangular prism Example

Question:

Find the volume of a rectangular prism whose length, width, and height are 8cm, 6cm, and 4cm, respectively.

Solution:

Given:

Length, l = 8 cm

Width, w = 6 cm

Height, h = 4 cm

The formula to find the volume of a rectangular prism is,

V = Length x Width x Height cubic units

V = 8 x 6 x 4 cm3

V = 192 cm3

Therefore, the volume of a rectangular prism is 192 cm3.

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