Question

the right pentagonal prism has a height of 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: Find the area of the base

The volume formula of a prism is \(V = B\times h\), 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 \(B\) by \(B=\frac{V}{h}\).

$$B=\frac{840}{14}=60$$

Step2: Use the formula for the area of a regular pentagon - like base (assuming it's a regular - like base for perimeter calculation, since for a prism with base area \(B\) and apothem \(a\) (here \(a = 4\)) and perimeter \(P\), the area formula of the base \(B=\frac{1}{2}Pa\))

We know \(B = 60\) and \(a = 4\). From \(B=\frac{1}{2}Pa\), we can solve for \(P\). Rearranging the formula gives \(P=\frac{2B}{a}\).

$$P=\frac{2\times60}{4}=30$$

Answer:

30 units