Volume formula is [tex]V = B \cdot h[/tex]
First find the area of the base (hexagon). The area of a hexagon can be found with the formula [tex]A = \frac{1}{2} P\cdot a[/tex] where [tex]a[/tex] is the apothem (line that's perpendicular to a side and connected to the center point) and [tex]P[/tex] is the perimeter.
We already know the length of the apothem (5.7 ft). We also have one side length already (6.58 ft), a hexagon has 6 sides, so [tex]P = 6\cdot 6.58 = 39.48[/tex] ft.
Plug these into the area formula
[tex]A = \frac{1}{2} (39.48)(5.7)[/tex]
Area of the base ([tex]B[/tex]) is 112.52 ft
Now plug into the volume formula using 15.4 ft as the height
Final answer:
[tex]V = 1732.81 ft^3[/tex]
