Question

1. what is the volume of a regular hexagonal prism with a base side length of 16 ft and a height of 9 ft?

Explanation:

Step1: Find the area of the base

The area formula for a regular hexagon is $A = \frac{3\sqrt{3}}{2}s^{2}$, where $s$ is the side - length of the hexagon. Given $s = 16$ ft.
$A=\frac{3\sqrt{3}}{2}\times16^{2}=\frac{3\sqrt{3}}{2}\times256 = 384\sqrt{3}$ square feet.

Step2: Calculate the volume of the prism

The volume formula for a prism is $V=Ah$, where $A$ is the area of the base and $h$ is the height. Given $h = 9$ ft.
$V=(384\sqrt{3})\times9=3456\sqrt{3}\approx3456\times1.732 = 5986.752$ cubic feet.

Answer:

$3456\sqrt{3}\text{ ft}^3\approx5986.75\text{ ft}^3$