A prism is a solid in which two congruent and parallel polygons from the top and the bottom faces. Prism are often distinguished by the shape of their base polygon. The octagonal prism is formed by square sides and two regular octagon bases. If all faces of octagonal prism are regular, it is a semiregular polyhedron.

Octagonal Prism

The octagonal prism is bounded by 2 octagonal faces and 8 squares. It has 24 edges and 16 vertices. volume of a octagonal prism is the area of hexagonal face times height.

Volume of Octagonal Prism
Volume of any prism,

Volume of a Prism = Al

Where, A is the area of base and l be the length of a prism.

In octagonal Prism,

Area of base of the octagonal prism (A) = 2ad

=> V = 2adl

Formula:

Volume of Octagonal Prism = Al = 2adl


Where, A = Area of base and 'l' be length of the prism.

For prisms, surface area is the sum of area of two bases and several parallelograms. Octagonal prism having front and back faces which are octagons and 8 rectangular faces.

For any prism,
Surface Area of a Prism = L + 2A

Where, L is the lateral surface area and A is the base area of the prism.

Octagonal Prisms

Lateral Surface area of the octagonal prism (L) = 8al

and area of base of the octagonal prism (A) = 2ad

Area of a Octagon

=> SA = 2A + 8al  

A = area of octagonal prism, a = side length of base and l = length of octagonal prism.

Formula:

Surface Area of an Octagonal Prism = 2A + 8al  


Where,
A = Area of octagonal prism
a = Side length of base and l = length of octagonal prism.

Below you could see some examples of octagonal prism:

Example 1:

The volume of an octagonal prism is 495 cubic millimeters. If the area of the base is 45 square millimeters, what is the height of the prism.

Solution:

Step 1:
Volume of the octagonal prism = 495 cubic millimeters
Area of base = 45 square millimeters
Height of the prism (h) = ?

Step 2:


Volume of octagonal prism = Ah
Where, A is the area of base and h be the height of a prism.

=> 495 = 45 x h

Step 3:

Solve for h,
Divide both side by 45

=> $\frac{495}{45} = \frac{45 h }{45}$

=> 11 = h

or h = 11

Hence the height of the octagonal prism is 11 millimeter.

Example 2 :

What is the volume and surface area of the 10 ft high regular octagonal prism whose each side 5 ft and area of base is 65 square ft.

Solution:
Step 1:

Area of base of the prism = 65 square ft
Height of the prism = 10 ft
Side of base = 5 ft

Step 2:

Volume of octagonal prism = Ah
Where, A is the area of base and h be the height of a prism.

=> V = 65 x 10

= 650

=> Volume pf the prism = 650 cubic ft.

Step 3:

Surface area of the prism = 2A + 8ah

A = area of octagonal prism, a = side length of base and h = height of octagonal prism.

=> SA = 2 x 65 + 8 x 5 x 10

= 130 + 400

= 530

=> Surface area of the octagonal prism is 530 square ft.
In right octagonal prism the lateral faces are each perpendicular to the plane of the base. A right prism means that the base and the height create a 90 degree.

Right Octagonal Prism