# Rectangular Prism

Rectangular Prism in mathematics is a three-dimensional geometric figure with four lateral faces and two parallel faces. A polygon that has two parallel bases is called a prism. A rectangular prism is one whose two parallel bases are rectangular. A rectangular prism is somewhat similar to a cuboid. A rectangular prism is observed by us in our daily life such as boxes, almirahs, etc. all resembling a rectangular prism.

Here, in this article, we have added the definition of a rectangular prism, formulas of a rectangular prism, that includes the surface area of a rectangular prism and volume of a rectangular prism, examples of rectangular prism formulas, and others in detail.

## What is a Rectangular Prism?

A rectangular prism in geometry is a polyhedron. It is a 3-D figure which has parallel bases. A rectangular prism is similar to a cuboid and has a total of six faces. There are three pairs of identical faces in a rectangular prism. The top and bottom faces of a rectangular prism are called the bases of the rectangular prism. The image added below shows a rectangular prism.

### Net of a Rectangular Prism

Net of a figure is the 2-D representation of the figure. Suppose we take a 3-D figure made of carbord and open it then the figure so obtained is called the net of 3-D figure.

The image showing net of a rectangular prism is added below,

### Faces Edges Vertices of a Rectangular Prism

In a rectangular prism we have 6 faces, 12 edges (sides) and 8 vertices. A rectangular prism is also called a cuboid and three sides of a rectangular prism intersect at right angles.

## Types of Rectangular Prism

Rectangular prism are categorised into two categories that are,

• Right Rectangular Prism
• Oblique Rectangular Prism

Right Rectangular Prism: A right rectangular prism is rectangular prism in which the base and top of rectangular prism are connected using right faces, i.e. they are connected using faces at right angle.

Oblique Rectangular Prism: A oblique rectangular prism is rectangular prism in which the base and top of rectangular prism are connected using faces, that are not connected using right faces, but are connected using Oblique faces.

The image added below shows the Right Recatngular Prism and Oblique Recatngular Prism

## Properties of Rectangular Prism

Various properties of rectangular prism are added below,

• A rectangular prism has 6 Faces, 8 Vertices, and 12 Edges.
• A rectangular prism has three dimension that are, Length, Width, and Height
• A rectangular prism has 3 pair of identical faces, etc.

## Rectangular Prism Formulas

Various formulas related to the rectanular prims are,

• Surface Area of a Rectanular Prism
• Volume of Rectangular Prism

Let’s learn about them in detail.

## Surface Area of Rectangular Prism

The surface area of a rectangular prism is equal to the total sum of the surface areas of all its faces. A rectangular prism has two types of surface areas that are,

• Lateral Surface Area
• Total Surface Area

Let’s learn about them in detail.

### Lateral Surface Area of Rectangular Prism

A rectangular prism’s lateral surface area can be found by calculating the sum of the areas of its four lateral faces, i.e., the total area of the prism excluding the areas of its two bases.

Lateral Surface Area Formula

The lateral surface area formula of rectangular prism is given as,

LSA of Rectangular Prism = 2h (l + b) square units

where,

• l is Length of Rectangular Prism
• b is Breadth of Rectangular Prism
• h is Height of Rectangular Prism

### Total Surface Area of Rectangular Prism

The total surface area of a rectangular prism is equal to the total sum of the surface areas of all its faces. Now, since it is composed of all rectangular faces, and the area of a rectangle is given by the product of its length and width, add up all the products of lengths and breadths to conjure up the surface area of a rectangular prism.

Total Surface Area Formula

The total surface area formula of rectangular prism is given as,

TSA of Rectangular Prism = 2(lb + lh + bh)

where,

• l is Length of Rectangular Prism
• b is Breadth of Rectangular Prism
• h is Height of Rectangular Prism

## Volume of Rectangular Prism

Volume of a rectangular prism is the total space occupied by the rectangular prism. The volume of rectangular prism is calculated using length, breadth, height of the rectangular prism, it unit is cubic unit, or unit3

Volume of Rectangular Prism(V) = l.b.h

where,

• l is Length of Rectangular Prism
• b is Breadth of Rectangular Prism
• h is Height of Rectangular Prism

## Examples on Rectangular Prism Formula

Example 1: Find the surface area of a rectangular prism if its length, breadth, and height are 4 m, 5 m, and 8 m.

Solution:

Given,

• l = 4 m
• b = 5 m
• h = 8 m

SA = 2(lb + lh + bh)

= 2(4 Ã— 5 + 4 Ã— 8 + 5 Ã— 8)

= 2(20 + 32 + 40)

= 2(92)

A = 184 m2

Example 2: Find the surface area of a rectangular prism if its length, breadth, and height are 2 m, 7 m, and 10 m.

Solution:

Given,

• l = 2 m
• b = 7 m
• h = 10 m

SA = 2(lb + lh + bh)

= 2(2 Ã— 7 + 2 Ã— 10 + 7 Ã— 10)

= 2(14 + 20 + 70)

= 2(104)

A = 208 m2

Example 3: Find the surface area of a rectangular prism if its length, breadth, and height are 9 m, 6 m, and 7 m.

Solution:

Given,

• l = 9 m
• b = 6 m
• h = 7 m

SA = 2(lb + lh + bh)

= 2(9 Ã— 6 + 7 Ã— 9 + 6 Ã— 7)

= 2(54 + 63 + 42)

= 2(159)

A = 318 m2

Example 4: Find the lateral surface area of a rectangular prism if its length, breadth, and height are 21 cm, 15 cm, and 18 cm.

Solution:

Given,

• l = 21 cm
• b = 15 cm
• h = 18 cm

LSA = 2h (l+ b)

= 2 Ã— 18 (21 +15)

= 36 Ã— 36

LSA = 1,296 cm2

Example 5: Find the volume of a rectangular prism if its length, breadth, and height are 7 m, 6 m, and 5 m.

Solution:

Given,

• l = 7 m
• b = 6 m
• h = 5 m

Volume of Rectangular Prism(V) = l.b.h

V = 7.6.5

V = 210 m3

The volume of rectangular prism is 210 m3

Example 6: Find the lateral surface area of a rectangular prism if its length, breadth, and height are 15 cm, 10 cm, and 13 cm.

Solution:

Given,

• l = 15 cm
• b = 10 cm
• h = 13 cm

LSA = 2h (l+ b)

= 2 Ã— 13 (15 + 10)

= 26 Ã— 25

LSA = 650 cm2

Example 7: Find the volume of a rectangular prism if its length, breadth, and height are 8 m, 5 m, and 9 m.

Solution:

Given,

• l = 8 m
• b = 5 m
• h = 9 m

Volume of Rectangular Prism(V) = l.b.h

V = 8.5.9

V = 360 m3

The volume of rectangular prism is 360 m3

## Practice Questions on Rectangular Prism

Q1: What is the volume of a rectangular prism with length 4 cm, width 7 cm and height 9 cm?

Q2: Find the Surface Area of a Rectangular Prism with length 3 cm, breadth 5 cm and height 6 cm.

Q3: What is the Surface Area of a Rectangular Prism with length 9 cm, width 12 cm and height 6 cm?

Q4: Find the volume of a Rectangular Prism with length 5.5 cm, width 4.5 cm and height 3.5 cm

## Rectangular Prism – FAQs

### 1. What is Formula to a Rectangular Prism?

Rectangular prims formulas are,

• LSA of Rectangular Prsim = 2.(w.h + h.l) square units
• TSA of Rectangular Prism = 2.(l.w + w.h + hl) square units
• Volume of Recatngular Prism = l.w.h cubic units

### 2. What is an Example of a Rectangular Prism in Math?

Examples of Rectangular Prism include,

• Box
• Almirah
• Fish Tank, etc.

### 3. What are the Faces, Edges and Vertices of a Rectangular Prism?

In a rectangular prism we have 6 Faces, 12 Edges, and 8 Corners.

### 4. What is a Square Rectangular Prism called?

A square prism is also called the Cuboid. In a square rectangular prism we have 4 rectangular faces and 2 square faces.

### 5. What is a Rectangular Prism?

A rectangular prism is a polyhedron with 6 faces. It is similar to a cuboid and has three pair of identical faces.

### 6. What is a Right Rectangular Prism?

Right Rectangular Prism is a prism in which the bases of the rectangular prism are at right angles.

### 7. What is Net of Rectangular Prism?

The net of rectangular prism is the 2-D representation of the rectangular prism.

### 8. What is Total Surface Area of a Rectangular Prism?

Total Surface Area(TSA) of the rectangular prism is the total space occupied by all the faces of the rectangular prism. It is given by the formula,

TSA of Rectangular Prism = 2.(lh + wh + lw)

### 9. What is Lateral Surface Area of a Rectangular Prism?

Lateral Surface Area(LSA) of the rectangular prism is the space occupied by all the lateral faces of the rectangular prism. It is given by the formula,

LSA of Rectangular Prism = 2.(lh + wh)

### 10. What is Volume of a Rectangular Prism?

Volume of a rectangular prism is the total space occupied by the rectangular prism in 3-D space. It is given by the formula,

Volume of Rectangular Prism = l.w.h

### 11. Can we find the Perimeter of Rectangular Prism?

We generally don’t find perimeter of a 3D Figure. However, if need to find the perimeter of a 3D figure for example a Rectangular Prism then we will add up the length of the edges.

### 12. How many sides does a Rectangular Prism Have?

A rectangular prism has 12 sides.

### 13. How many Face does a Rectangular Prism Have?

A rectangular prism has 6 rectangular faces.

### 14. How many Vertex does a Rectangular Prism Have?

A rectangular prism has 8 vertices.

### 15. How to Find the Area of a Rectangular Prism?

Area of Rectangular Prims is calculated using the Surafce area formula

• LSA of Rectangular Prsim = 2.(w.h + h.l) square units
• TSA of Rectangular Prism = 2.(l.w + w.h + hl) square units

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