# What is a Rectangular Prism? Definition With Examples

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases.

A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

## Real-Life Examples

A pencil box and a book are rectangular prisms. It may surprise you, but your room is also a cuboid or a rectangular prism.

## Properties of a Rectangular Prism:

• A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces.
• All the opposite faces of a rectangular prism are congruent.
• A rectangular prism has a rectangular cross section.

## Types of Rectangular Prisms

There are two types of rectangular prisms:

1. Right Rectangular Prism: The angle formed by the faces with any of its bases is 90° or a right angle. All the faces, including the lateral ones, are rectangular.
2. Non-Right (Oblique) Rectangular Prism: The faces of such a prism are not at right angles to the bases. The shape of each face is more like a parallelogram than a perfect rectangle.

## Surface Area and Volume of a Rectangular Prism:

The rectangular prism has three dimensions. It means that it has a surface area and volume.

Since all the faces of a rectangular prism are rectangles and opposite faces are equal, the surface area of a rectangular prism can be calculated using the following formula:

Total Surface Area $= 2 {(\text{width} \times \text{length} ) + (\text{length} \times \text{height}) + (\text{width} \times \text{height})}$

Lateral Surface Area $= 2 {( \text{length} \times \text{height} ) + (\text{width} \times \text{height} )}$

Volume of a rectangular prism is simply obtained by multiplying all three dimensions $–$ length, height and width.

Volume $= \text{length} \times \text{width} \times \text{height}$

## Fun Facts

– Rectangular prisms are the most commonly used prisms in real life, especially in packaging, from cereal boxes to cartons and parcels delivered by mail.

## Solved Examples

1. Find the volume of a right rectangular prism whose length $= 8$ cm, width $= 5$ cm, and height $= 16$ cm.

Volume $=$ (LWH)

$= 8516$

$= 640$ cm3

1. What is the total surface area of a right rectangular prism with length $= 5$ feet, width $= 4$ feet, and height $= 6$ feet.

Total surface area $= 2 { (\text{WL})+(\text{LH})+(\text{WH})}$

Total surface area $= 2 {(45)+(56)+(46)}$

$= 2(20+30+24)$

$= 148$ ft2

1. The dimensions of a rectangular prism are length = 2.5 cm, width = 4.5 cm, and height = 1.5 cm. Find the volume.

Volume $=$ LWH

$= 2.5 4.5 1.5$

$= 16.875$ cm3

1. For a rectangular prism, length $= 4$ feet, width $= 4$ feet and height $= 9$ feet. Find the lateral surface area.

Lateral surface area $= 2 { (\text{LH})+(\text{WH})}$

Lateral surface area $= 2 { (49)+(49)}$

$= 2 ( 36+36 ) = 144$ ft2

## Practice Problems

1

### What is the volume of a rectangular prism whose dimensions are length $= 2$ cm, width $= 2$ cm, and height $= 4$ cm?

$16 \text{cm}^3$
$12 \text{cm}^3$
$44 \text{cm}^3$
$10 \text{cm}^3$
CorrectIncorrect
Correct answer is: $16 \text{cm}^3$
Volume $= 2 \times 2 \times 4 = 16 \text{cm}^3$
2

### The volume of a rectangular prism is $50 \text{cm}^3$. Also, length $= 2$ cm and width $= 5$ cm. What is its height?

45 cm
3 cm
5 cm
9 cm
CorrectIncorrect
$h$ $= \frac{V}{(l \times w)} =\frac{50}{(2\times5)}=5$ cm
3

### The dimensions of a rectangular prism are length $= 4$ cm, width $= 6$ cm and height $= 10$ cm. What is the total surface area?

$248 \text{cm}^2$
$124 \text{cm}^2$
$100 \text{cm}^2$
$50 \text{cm}^2$
CorrectIncorrect
Correct answer is: $248 \text{cm}^2$
Total Surface Area $=$ $2{(4\times6)+(6\times10)+(10\times4)} =248 \text{cm}^2$
4

### The dimensions of a rectangular prism are length $= 5$ cm, width $= 6$ cm and height $= 7$ cm. What is the lateral surface area?

$248 \text{cm}^2$
$154 \text{cm}^2$
$100 \text{cm}^2$
$50 \text{cm}^2$
CorrectIncorrect
Correct answer is: $154 \text{cm}^2$
Lateral Surface Area $=$ $2\times{ (5\times7)+(6\times7) } = 154 \text{cm}^2$