Question 1203310
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To start with, the problem is deficient in not stating that the base of the pyramid is a REGULAR hexagon.<br>
Next, it is not clear what "base... being 5 units" means.<br>
Finally, the problem is overprescribed when the "base", volume, and height of the pyramid are all given and are not consistent.<br>
The only possible way to solve the problem is to ignore one of the given pieces of information.  Since it is not clear what a "base of 5" means, I will ignore that.<br>
So my GUESS as to the correct information in the problem is a pyramid with a regular hexagonal base, a height of 10, and a volume of 750.  Then....<br>
{{{V = (1/3)(B)(h)}}}
{{{750 = (1/3)(B)(10)}}}
{{{B= 225}}}<br>
ASSUMING the hexagonal base is regular, each of the equilateral triangles that comprise the base have area 225/6 = 37.5.  In terms of the length a of the apothem, that area (one-half base, times height) is {{{A=(a/sqrt(3))(a)}}}.  So<br>
{{{37.5=a^2/sqrt(3)}}}
{{{a^2=37.5*sqrt(3)}}}<br>
In exact form, the length of the apothem (with all the assumptions that have been made) is<br>
{{{sqrt(37.5*sqrt(3))}}}<br>
That's 8.06 to 2 decimal places.<br>
Again, however, note that the presentation of the problem is exceedingly poor....<br>