Question

the right pentagonal prism has a height of 14 units. the volume of the prism is 840 cubic units. what is the perimeter of the base? 12 units 15 units 21 units 30 units

Explanation:

Step1: Recall volume formula

The volume formula for a prism is $V = Bh$, where $V$ is volume, $B$ is the area of the base, and $h$ is the height. Given $V = 840$ and $h=14$, we can find the area of the base.
$B=\frac{V}{h}$
$B=\frac{840}{14}=60$

Step2: Recall area - perimeter relationship for regular pentagon

For a regular pentagon, the area formula in terms of the apothem $a$ (assume the apothem is 4 as it seems to be indicated in the non - clear part of the image) and perimeter $P$ is $B=\frac{1}{2}aP$. We know $B = 60$ and $a = 4$.
$P=\frac{2B}{a}$
$P=\frac{2\times60}{4}=30$

Answer:

D. 30 units