The prism with the pentagonal base's volume is 585 cm³.
Step-by-step explanation:
Step 1:
The prism has a pentagonal base.
The volume of a prism with a pentagonal base, [tex]V=\frac{1}{4} \sqrt{5(5+2 \sqrt{5})} a^{2} h.[/tex]
In the formula to determine the prism's volume, in the question, it is given that [tex]\frac{1}{4} \sqrt{5(5+2 \sqrt{5})} a^{2}[/tex] is equal to 45 cm².
Step 2:
So if we substitute [tex]\frac{1}{4} \sqrt{5(5+2 \sqrt{5})} a^{2} = 45[/tex] in [tex]V=\frac{1}{4} \sqrt{5(5+2 \sqrt{5})} a^{2} h.[/tex] we get,
[tex]V=\frac{1}{4} \sqrt{5(5+2 \sqrt{5})} a^{2} h =[/tex] [tex]45h.[/tex]
The value of h for the given prism is 13 cm, so
[tex]V = 45(13) = 585[/tex] cm³.
The prism's volume is 585 cm³.
