Octagonal Prisms: Paper Models, Surface Area, Volume Formulas and Nets

Everything you ever wanted to know about octagonal prisms. Whether you’re a student learning about polyhedrons for the first time, or a parent who needs a recap, by the time you get to the end of this webpage, you’ll be an expert.

Octagonal Prism Wireframe

Octagonal Prism Definition

An octagonal prism is a 3D object with two regular octagon caps and rectangular or square sides.

Octagonal Prism Images
Examples of Octagonal Prisms

Octagonal Prism Paper Model and Net

Below is a free printable octagonal prism net. Please open the pdf file by clicking on the image below. Then you will be able to download the file in your browser. (If you are unable to see the PDF, you may need an updated version of Adobe Acrobat Reader.)

Octagonal Prism Paper Model Net

Construction Tutorial

Printer
1. Print the template on some sturdy construction paper.
Scissors
2. Cut out the prism net along its perimeter. Fold along the lines of the flaps and shapes that make up the net.
Tape
3. Fold the pieces of the prism so that the octagon caps are facing. Tape the flaps under the faces with scotch tape. Once all the flaps are taped, your octagonal prism paper model is complete.

Octagonal Prism Surface Area Formulas

Octagon Base and Rectangle

Octagonal Prism Surface Area Formula:
8 R+ 2B
Where:
R = the Area of a Rectangle Face
B = the Area of an Octagon Face

The surface area of a prism is equal to the sum of the areas of its faces. An octagonal prism is made up of 8 rectangle faces and 2 octagon faces.

If you happen to know R and B, then you’re all done. But what if you only know the length of a few sides of the octagonal prism? No problem. Let’s take a look.

 

 

Octagon Lengths

Octagonal Prism Surface Area Formula:
8al+ 4ad
Where:
a = the length of an octagon edge
l = the length of the octagonal prism

d = the width of an octagon face

Notice that the first and second formulas are actually the same, since:

R =al

B=2ad

Instead of 8R +2B, we get: 8(al) + 2(2ad) which is equal to the second formula: 8al+ 4ad

 

 

Octagonal Prism Volume Formulas

Octagon Face and Edge

Octagonal Prism Volume Formula:
Volume =Bl
Where:
B = the Area of an Octagon Face
l = the length of the octagonal prism

Octagonal Prism Volume Formula:
Volume =2adl
Where:
a = the length of an octagon edge
l = the length of the octagonal prism
d = the width of an octagon face

Notice that the first and second formulas are actually the same, since:

B=2ad

Instead of Bl, we get: (2ad)l which is equal to the second formula: 2adl

Vertices, Faces, and Edges

An octagonal prism has 16 vertices, 10 faces, and 24 edges.

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