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Rectangular Prism – Definition With Examples

Camille Ira B. Mendoza

reviewed by Jo-ann Caballes

Updated on October 8, 2024

A prism is a three-dimensional mathematical shape with parallel bases and sides.

There are various kinds of prisms, but here we will be discussing rectangular prisms, their meaning, types, and so on.

What is a Rectangular Prism?

A rectangular prism is a three-dimensional shape with six surfaces; one on top, one at the base, and four side surfaces. Each of these faces is rectangular, hence its name Rectangular prism. It is also called a cuboid,

Rectangular prism: definition

The rectangular prism is a 3-dimensional shape, with 6 rectangular surfaces, 8 corners, and 12 edges.

How many sides does a rectangular prism have?

The rectangular prism has 6 sides. All of these sides are rectangular and the opposite sides are identical.

What does a rectangular prism look like?

As we mentioned earlier, a rectangular prism is a shape that has 6 rectangular faces. A notebook is a rectangular prism, so is a door, and a room.

Below are some other examples of rectangular prism shapes: 

• Geometry box
• A fish tank
• A shoe box
• A cereal box
• Refrigerator
• Computer, etc.

Properties of a Rectangular Prism:

The following are some deciding variables that tell if a shape or item is a rectangular prism or not:

• To be a 3-dimensional shape, a rectangular prism has length, width, and height
• A rectangular prism has 6 sides, 8 vertices, and 12 edges.
• All surfaces are rectangular in shape
• All opposite surfaces are identical

How many vertices does a rectangular prism have?

There are 8 rectangular prism vertices. The vertices are the corners where the faces meet to form the shape.

Types of Rectangular Prisms

The rectangular prism can be of two types:

• Right rectangular prism
• Oblique rectangular prism

What is a right rectangular prism?

A  right rectangular prism forms a right angle of 90° when it intersects at the base. All the sides are rectangular. It is the most common instance of rectangular prisms. A book is an example.

What is a non-right or oblique rectangular prism?

An oblique rectangular prism has diagonal side surfaces, which gives the prism a sideways appearance like a parallelogram. A window with a tilted design can be considered a non-right rectangular prism.

Formula for surface area and volume of a rectangular prism

The rectangular prism has 2 kinds of surface areas:

• Lateral surface area
• Total surface area

Lateral Surface Area

For this formula, we add the lateral side faces and exclude the top and base:                

LSA = 2 (l × h) + (w × h) 

LSA = 2 (lh + wh)

Total Surface Area

The total surface area, however, is calculated by adding the multiplied result of all the six surfaces (not just the lateral sides) :

TSA = 2 (width × length) + (width × height) +( length × height) 

The formula for finding the total  surface area can be shortened to: 

TSA = 2 (wl + wh + lh)

Volume 

The formula for finding the volume is the product of the length, height, and width of a rectangular prism:

V =  l × h × w

V = lhw

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Solved Maths Tasks: Examples

Solved math problem 1

What kind of rectangular prism has a width of 6 ft, a length of 5 ft, and a height of 7 ft that happens to be slanted?

Answer

Solved math problem 2

When a rectangular prism has the following characteristics:

Length = 8 feet

Height =  10 feet

Width = 9 feet

What is the total surface area and lateral surface area?

Answer

TSA = 2 (wl + wh + lh)

= 2 (9 × 8 + 9 × 10 + 8× 10)

= 2 (242)

LSA = 2 (lh + wh)

= 2 (8 × 10 + 9 × 10)

= 2 (170)

Solved math problem 3

Find the volume of a right rectangular prism when:

Length = 3.5 cm

Width = 7.5 cm

Height = 1.5 cm

Answer

V =  l × h × w

V = 3.5 × 1.5 × 7.5

V = 39.37 cm3 

Rectangular Prism: Practice Math Problems

Rectangular Prism: worksheets

Learn more about prisms and geometry, generally with Brighterly’s free worksheets:

• Geometry worksheets
• Area of a triangle worksheet
• Parallel and perpendicular worksheets
• Rectangle worksheets

Camille Ira B. Mendoza

17 articles

I am a seasoned math tutor with over seven years of experience in the field. Holding a Master’s Degree in Education, I take great joy in nurturing young math enthusiasts, regardless of their age, grade, and skill level. Beyond teaching, I am passionate about spending time with my family, reading, and watching movies. My background also includes knowledge in child psychology, which aids in delivering personalized and effective teaching strategies.