Question

HELP PLEASE BE QUICK

Answer 1

The prism with the pentagonal base's volume is 585 cm³.

Explanation:

Step 1:

The prism has a pentagonal base.

The volume of a prism with a pentagonal base,
`V=(1)/(4) \sqrt{5(5+2 √(5))} a^(2) h.`

In the formula to determine the prism's volume, in the question, it is given that
`(1)/(4) \sqrt{5(5+2 √(5))} a^(2)` is equal to 45 cm².

Step 2:

So if we substitute
`(1)/(4) \sqrt{5(5+2 √(5))} a^(2) = 45` in
`V=(1)/(4) \sqrt{5(5+2 √(5))} a^(2) h.` we get,

`V=(1)/(4) \sqrt{5(5+2 √(5))} a^(2) h =`
`45h.`

The value of h for the given prism is 13 cm, so

`V = 45(13) = 585` cm³.

The prism's volume is 585 cm³.