Table of Contents

Last modified on August 3rd, 2023

An octagonal prism is a three-dimensional solid consisting of two identical octagonal bases joined together by eight rectangular faces. It has 10 faces (2 octagonal and 8 rectangular), 24 edges, and 16 vertices.

The shape of birdhouses and chocolate boxes are some examples of octagonal prism in real life.

Like all other polyhedrons, we can calculate the surface area and volume of a regular octagonal prism.

The surface area, also known as the total surface area, of an octagonal prism is the entire space occupied by its outermost layer (or faces). It is measured in square units such as m^{2}, cm^{2}, mm^{2}, and in^{2}. The formula is given below:

As we know,

**Total Surface Area (****TSA****) = 2 × Base Area + Base Perimeter × height**

Also**, **since **Lateral Surface Area ( LSA)**

Here, Base Perimeter = *8**ah*

∴ **Lateral Surface Area (****LSA) = ****8****ah**

Thus, we can write

**Total Surface Area ( TSA) = **

Let us solve an example to understand the concept better.

**Find the lateral and total surface area of an octagonal prism with a base edge of 2 cm and height of 5 cm.**

Solution:

As we know,

Lateral Surface Area (*LSA) = 8ah, here a = 2 cm, h = 5 cm*

∴ *LSA = *8 × 2 × 5

= 80 cm^{2}

Total Surface Area (*TSA*) = ${4\left( 1+\sqrt{2}\right) a^{2}+LSA}$, here a = 2 cm, *LSA *= 80 cm^{2}

${\therefore TSA=4\left( 1+\sqrt{2}\right) 2^{2}+80}$

= 118.63 cm^{2}

The volume of an octagonal prism is the space it occupies in the three-dimensional plane. It is measured in cubic units such as m^{3}, cm^{3}, mm^{3}, ft^{3}. The formula is given below:

Let us solve some examples to understand the concept better.

**Find the volume of an octagonal prism whose base edge is 6 cm and height is 7 cm.**

Solution:

As we know,

Volume* (V) *= ${2\left( 1+\sqrt{2}\right) a^{2}h}$, here *a* = 6 cm, *h* = 7 cm

${\therefore V=2\left( 1+\sqrt{2}\right)\times 6^{2}\times 7}$

= 1216.76 cm^{3}

Finding the volume of an octagonal prism when **APOTHEM**, **BASE** **EDGE** and **HEIGHT** are known

**Find the volume of an octagonal prism whose base edge is 4 cm, apothem is 4.828 cm, and height is 5 cm.**

Solution:

Here we will use an alternative formula.

Volume* (V) *= 4 × base edge × apothem × height, here base edge = 4 cm, apothem = 4.828 cm, height = 5 cm

∴*V* = 4 × 4 × 4.828 × 5

= 386.24 cm^{3}

**More Resources:**- Volume of a Prism
- Surface Area of a Prism
- Right Prism
- Oblique Prism
- Rectangular Prism
- Volume of a Rectangular Prism
- Surface Area of a Rectangular Prism
- Triangular Prism
- Volume of a Triangular Prism
- Surface Area of a Triangular Prism
- Hexagonal Prism
- Volume of a Hexagonal Prism
- Surface Area of a Hexagonal Prism
- Pentagonal Prism
- Volume of a Pentagonal Prism
- Surface Area of a Pentagonal Prism
- Trapezoidal Prism
- Volume of a Trapezoidal Prism
- Surface Area of a Trapezoidal Prism
- Square Prism
- Volume of a Square Prism
- Surface Area of a Square Prism
- Octagonal Prism
- Heptagonal Prism
- Decagonal Prism

Last modified on August 3rd, 2023