 # Rectangular Prism

In Mathematics, Geometry is the study of shapes and configuration of objects. A rectangular prism is a polyhedron with two congruent and parallel bases. It is also a cuboid. It has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism. Similar to triangle, square and pentagonal prism, it also has its surface area. The surface area of the prism is the area of its net. 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. ### Properties of Rectangular Prism

• It has 6 rectangular faces, 12 edges and 8 vertices.
• Opposite faces are in rectangle shape
• It has a rectangular cross-section
• It looks exactly like a cuboid

## Types

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. ## Formulas

A rectangular prism is a three-dimensional object. Hence, it will have its surface area and volume dimensions. To calculate the area of a prism, we have to know the length of its sides or edges. 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 = Px h Square units

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 Net

The net of any prism is the surface area of it. It shows when we open the prism in a plane; then all its sides could be visible at the same time. If we calculate the individual area of all its sides using the net, we will get the total surface area. See the figure below to find the net for the rectangular prism. You can see from the above figure, all the sides of the prism are in a rectangular shape. By using the formula for the area of rectangle, you can find the areas for each face and add all the areas to get the net of the prism.

### Rectangular prism Example

Question 1: 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.

Question 2: Find the area 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 area of a rectangular prism is,

A = 2 (lh +wh + lw )

A = 2 (8×4+6×4+8×6)

A = 2(32+24+48)

A = 2(104)

A = 208 sq.cm.

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