To solve this, we must understand how to find the formula of a hexagon (a 6 sided figure) and how to find volume. We will start with finding the area of a hexagon, because it is more difficult.
The formula for area of a regular hexagon is
[tex] \frac{3 \sqrt{3}}{2}a^{2}[/tex] where "a" is any given side length of the hexagon. Therefore, we can just substitute in 12 for "a" and solve as normal.
[tex] \frac{3 \sqrt{3}}{2}12^{2} = 374.123[/tex]
Now for solving volume. To solve for volume, we must multiply the area by the height. This accounts for the entire shape for every unit of height.
374.123*15=5611.845
Using the math above, we can see that the volume of this figure is 5611.845 cubic feet.
