SOLUTION: how do i find the volume of a hexagonal pyramid? The Height is 31'-0" and the sides are 21'-0" apart. Thank you

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Question 11393: how do i find the volume of a hexagonal pyramid? The Height is 31'-0" and the sides are 21'-0" apart.
Thank you
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a regular pyramid is found by multiplying the area of the base by the height of the pyramid and dividing by 3. V+=+%281%2F3%29Bh B = area of base.
You are given the height (31') but I'm having trouble figuring out what you mean by..."the sides are 21' apart"
If you know the length of each side of the hexagonal base, you can find its area. Also, if you know the length of the apothem of the hexagonal base, you can find the area.
Let's assume that the length of each side of the hexagonal base is 21'.
The area of a regular polygon, in terms of the length of the sides, is given by:
A+=+%281%2F4%29ns%5E2cot%28180%2Fn%29 Where: n = number of sides (6) and s = length of side (21')
A+=+%281%2F4%29%286%29%2821%5E2%29cot%28180%2F6%29
A+=+%281%2F4%29%286%29%28441%29cot%2830%29
A+=+%28661.5%29%281.732%29
A+=+1145.75 Now multiply this by the height and divide by 3 to find the volume
V+=+%281%2F3%291145.75%2831%29
V+=+11839.43 Cubic feet.