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Octagonal Prism – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Octagonal PrismOctagonal Prism – Definition, ExamplesTable of ContentsOctagonal Prism — Definition With Examples Definition of Octagonal Prism

A prism is a closed solid shape with two identical faces that are parallel polygons, while the side faces are either parallelograms or rectangles. All faces of a prism are flat. Prisms come in various types based on their base shapes, such as triangular prism, rectangular prism (also known as cuboid), cube (or square prism), and pentagonal prism.

An octagonal prism is a specific type of prism that has 2 octagonal bases and 8 rectangular sides. It contains a total of 10 faces, 24 edges, and 16 vertices. The surface area of an octagonal prism includes the area of all its faces, with the total surface area formula being lateral surface area (perimeter of base ××× height) plus twice the base area. The volume of an octagonal prism is calculated by multiplying the base area by the height. For a regular octagonal prism with side length (sss), height (hhh), and apothem length (aaa), the volume formula is 4sah4sah4sah.

Examples of Octagonal Prism Example 1: Counting the Faces of an Octagonal Prism Problem:

How many faces does an octagonal prism have?

Octagonal prism

Step-by-step solution: Step 1, Understand what faces are. The faces are the surfaces that make up a 3D shape. Step 2, Count the different types of faces. An octagonal prism has 8 rectangular faces (the lateral faces) and 2 octagonal faces (the bases). Step 3, Add up all the faces. 8+2=108 + 2 = 108+2=10 faces. Example 2: Finding the Edges of an Octagonal Prism Problem:

How many edges does an octagonal prism have?

Octagonal prism

Step-by-step solution: Step 1, Recall that edges are the lines where two faces meet. Step 2, Count the edges around each octagonal base. Each octagon has 8 edges. Step 3, Count the edges connecting the two bases. There are 8 vertical edges connecting the top and bottom bases. Step 4, Add all edges together. 8+8+8=248 + 8 + 8 = 248+8+8=24 edges. Example 3: Calculating the Volume of a Regular Octagonal Prism Problem:

What is the volume of the given regular octagonal prism? (Given: side = 6 m, apothem = 4 m, height = 12 m)

Regular octagonal prism

Step-by-step solution: Step 1, Find the perimeter of the base. For a regular octagon, perimeter =8×= 8 ×=8× side. So, perimeter =8×6= 8 \times 6=8×6 m =48= 48=48 m. Step 2, Calculate the area of the base. Area of base === perimeter ××× apothem ÷2÷ 2÷2. So, area =48 m×4 m÷2=96 m2= 48 \text{ m} \times 4 \text{ m} \div 2 = 96 \text{ m}^2=48 m×4 m÷2=96 m2. Step 3, Apply the volume formula. Volume === base area ××× height. So, volume =96 m2×12 m=1,152 m3= 96 \text{ m}^2 \times 12 \text{ m} = 1,152 \text{ m}^3=96 m2×12 m=1,152 m3. Comments(7)MMathTutorAbbyNovember 5, 2025This definition of octagonal prism was super helpful! It made explaining 3D shapes to my students a breeze. Thanks!

SSoccerFanOscarNovember 4, 2025This definition of octagonal prism was super helpful! I used it to explain the shape to my students, and they finally got it.

MCMs. CarterSeptember 17, 2025This definition of an octagonal prism was super clear and easy for my kids to understand! We even used the examples to build a paper model—great hands-on learning. Thanks for making math fun!

NNatureLover75September 10, 2025I used the octagonal prism definition and examples to help my kids with their geometry homework, and it worked wonders! The step-by-step details made it so easy to explain. Thanks for this resource!

NNatureLover85August 26, 2025I used this page to help my kids understand 3D shapes, and the clear definition and examples of an octagonal prism made it super easy! We even built one out of cardboard—fun and educational!

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