Answer:
Volume = 928.8 in³
Explanation:
First, we need to find the apothem of the pentagon. So, the apothem of a regular polygon is equal to:
[tex]a=\frac{s}{2\tan (\frac{180}{n})_{}}[/tex]
Where s is the length of the sides and n is the number of sides of the polygon.
So, replacing s by 6 in and n by 5, we get:
[tex]\begin{gathered} a=\frac{5}{2\tan(\frac{180}{5})} \\ a=\frac{5}{2\tan (36)} \\ a=\frac{5}{2(0.73)} \\ a=\frac{5}{1.45}=3.44 \end{gathered}[/tex]
Now, the area of the pentagon will be equal to:
[tex]A=\frac{p\times a}{2}[/tex]
Where p is the perimeter of the pentagon. In this case, the perimeter is equal to:
p = 5 x 6 in = 30 in
Therefore, the area of the pentagon is:
[tex]A=\frac{30\times3.44}{2}=51.6in^2[/tex]
Finally, the volume of the prism will be equal to:
Volume = Area x Height
Volume = 51.6 in² x 18 in
Volume = 928.8 in³
