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 for prism

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 $V = 840$ cubic - units and $h=14$ units. We can find the area of the base $B$.
$B=\frac{V}{h}$
$B = \frac{840}{14}=60$ square units.

Step2: Recall formula for area of pentagonal base

The area formula for a regular pentagonal base in terms of the apothem $a$ (the distance from the center of the pentagon to the mid - point of a side) and perimeter $P$ is $B=\frac{1}{2}aP$. Given that the apothem $a = 4$ units.
We can solve for the perimeter $P$ using the formula $P=\frac{2B}{a}$.
Substitute $B = 60$ square units and $a = 4$ units into the formula:
$P=\frac{2\times60}{4}=30$ units.

Answer:

30 units