Question

Medal and fan for geometry help.

Answer 1

@welshfella

Answer 2

Find the area of the base. It's a regular hexagon.

Answer 3

The formula is \[\frac{ 3\sqrt{3} }{ 2 }*a^2\] ?

Answer 4

Okay, is 'a' 8.7 or 10 or something else?

Answer 5

10

Answer 6

I think that it is:
\[\Large \begin{gathered}
base\;area = \frac{{perimeter \times apothem}}{2} = \hfill \\
\hfill \\
= \frac{{\left( {10 \times 6} \right) \times 8.7}}{2} = ...? \hfill \\
\end{gathered} \]

Answer 7

261

Answer 8

ok!
and the requested volume is:
\[\Large \begin{gathered}
volume = base\;area \times height = \hfill \\
\hfill \\
= 261 \times 7 = ...? \hfill \\
\end{gathered} \]

Answer 9

1827

Answer 10

that's right!

Answer 11

I didn't expect the previous formula to be similar to this figure.

Answer 12

yes! Such formulas are very similar each to other at a first sight

Answer 13

@Michele_Laino

Answer 14

here we have to compute the base area first, in order to do that, we can apply the Eron's formula:
the half perimeter of the base triangle, is:
\[\Large p = \frac{{10 + 8 + 6}}{2} = ...?\]

Answer 15

12

Answer 16

correct!

Answer 17

so the area of the base triangle, is:
\[\Large \begin{gathered}
area = \sqrt {p\left( {p - a} \right)\left( {p - b} \right)\left( {p - c} \right)} = \hfill \\
\hfill \\
= \sqrt {12 \times \left( {12 - 10} \right) \times \left( {12 - 8} \right) \times \left( {12 - 6} \right)} = ...? \hfill \\
\end{gathered} \]

Answer 18

576

Answer 19

ok! we have:
\(area= \sqrt 576=24\)
now the requested volume is:
\[\Large volume = \frac{{24 \times 8}}{3} = ...?\]

Answer 20

64

Answer 21

that's right!

Answer 22

I'm very sorry I have to go out now

Answer 23

I never liked esoteric formulas. Just build the thing.

One of the six triangles that makes the base: \(\dfrac{1}{2}\cdot (10\;ft)\cdot(8.7\;ft) = 43.5\;ft^{2}\)

There are 6 of these: \(43.5\;ft^{2}\cdot 6 = 261\;ft^2\). This is the area of the base.

\(261\;ft^{2}\cdot 7\;ft = 1827\;ft^{3}\) This is the volume.

Answer 24

here I am

Answer 25

that's right, the requested volume is \(64\)

Answer 26

the base area can be computed noting that the triangle is a right triangle, so we have:
area=\((6 \times 8) /2=24\)

Answer 27

alright

Answer 28

:)