Answer:
To find the volume of an octagonal prism, calculate the area of the octagonal base, then multiply this by the height of the prism.
Step-by-step explanation:
The volume of a prism can be found by multiplying the area of its base by its height.
[tex]\boxed{\sf Volume\;of\;a\;prism=Area_{base} \times height}[/tex]
Therefore, to find the volume of an octagonal prism, calculate the area of the octagonal base, then multiply this by the height of the prism.
The formula for the area of a regular octagon given its side length, s, is:
[tex]\boxed{\textsf{Area of a regular octagon}=(2+2\sqrt{2})s^2}[/tex]
Therefore, the formula for the volume of a regular octagonal prism, given the side length, s, and the height, h, is:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Volume of a regular octagonal prism}\\\\$V=(2+2\sqrt{2})hs^2$\\\\where:\\\phantom{ww} $\bullet$ $s$ is the side length of the regular octagonal base.\\\phantom{ww} $\bullet$ $h$ is the height of the prism.\\ \end{minipage}}[/tex]
