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.**