Question

Please help...

working on a find a volume problem for a right hexagonal pyramid and can't figure what I did wrong

Answer 1

\(V=\dfrac{1}{3}\color{tomato}{B}\color{lime}{h}\)
so you got the equation correct, now lets go through your steps,
your equation:

\(A=(2.5\sqrt{3})(30)\) now, I don't understand where you got this from

when the equation to find the base \(B\) is
\(A=\dfrac{3\sqrt{3}}{2}a^2\) which you would just plug in 5 for a and solve to find the base
\(A=\dfrac{3\sqrt{3}}{2}\color{lime}{(5)}^2\)

so from this, you would add the answer to \(B\) into your equation,
\(V=\dfrac{1}{3}\color{tomato}{B}h\)

now you would just add in your height (the dotted line in the middle) and then solve it.

Answer 2

@extrinix rechecked the formula then figured that out right now thanks for explaining my error appreciate it!

Answer 3

You're welcome.

Answer 4

base height
\[=\sqrt{5^2-(\frac{ 5 }{ 2 })^2}=\frac{ 5\sqrt{3} }{ 2 }\]
area of base
\[=6 \times \frac{ 1 }{ 2 }\times 5 \times \frac{ 5\sqrt{3} }{ 2}=\frac{ 75\sqrt{3} }{2 }\]
volume
\[=\frac{ 1 }{ 3 } base~area~\times height\]
\[=\frac{ 1 }{ 3 }\times \frac{ 75\sqrt{3} }{ 2 }\times 7=\frac{ 175\sqrt{3} }{ 2 }\approx 151.55 \]