Question

type the correct answer in the box. use numerals instead of words. a regular pentagonal prism has a volume of 4,560 cubic millimeters. what is the height of the prism? the height of the prism is millimeters.

Explanation:

Step1: Calculate base - area

The base is a regular pentagon. The area formula for a regular pentagon is $A=\frac{1}{2}\times perimeter\times apothem$. The perimeter of the pentagon with side - length 12 mm is $P = 5\times12=60$ mm, and the apothem is 8 mm. So, $A=\frac{1}{2}\times60\times8 = 240$ $mm^{2}$.

Step2: Find height

The volume formula for a prism is $V = A\times h$. Given $V = 4560$ $mm^{3}$ and $A = 240$ $mm^{2}$, we can solve for $h$. $h=\frac{V}{A}=\frac{4560}{240}=19$ mm.

Answer:

19