Question

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Answer 1

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, $V=\frac{1}{4} \sqrt{5(5+2 \sqrt{5})} a^{2} h.$

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

Step 2:

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

$V=\frac{1}{4} \sqrt{5(5+2 \sqrt{5})} a^{2} h =$ $45h.$

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

$V = 45(13) = 585$ cm³.

The prism's volume is 585 cm³.