Question

Can anyone help? So confused!!

a hexagonal tray of vegetables has an area of 450 cm^2. What is the length of each side of the hexagon? Also, what is the area at the bottom in terms of the side length?

Answer 1

Does anyone know how to do this??

Answer 2

@phi can you help?

Answer 3

do you know the formula for the area of a hexagon ?

Answer 4

no I don't

Answer 5

see wikipedia
http://en.wikipedia.org/wiki/Hexagon#Regular_hexagon

for a formula that gives the area as a function of the length of a side

Answer 6

ok

Answer 7

do you see the formula ?

Answer 8

yes, but it sure looks confusing.

Answer 9

\[ A = \frac{3\sqrt{3}}{2} t^2 \]
where t is the length of 1 side

Answer 10

multiply both sides by the reciprocal of 3sqrt(3)/2 to get t^2 by itself

Answer 11

ok

Answer 12

so would I end up with 450 cm^2 times t^2

Answer 13

oh wait, I messed up. nevermind

Answer 14

write down your steps

Answer 15

2/3^3(450cm^2) = 2/3^3(3^3/2)

Answer 16

and don't forget the side call it s^2 (not sure why wiki uses t^2)
2/3^3(450cm^2) = s^2 (the other stuff cancels out)

now simplify the left side

Answer 17

\[ \frac{2 \cdot 450}{3 \sqrt{3} } = s^2 \]

Answer 18

900/3^3 = s^2

Answer 19

oops I didnt mean 3^3 I meant 3 sqrt 3

Answer 20

you could divide 3 into 900, right ?
and I would multiply top and bottom by sqrt(3) to move the sqrt up top

Answer 21

yeah 3 into 900 is 300

Answer 22

multiply top and bottom by sqrt(3)

Answer 23

1558.8/9

Answer 24

900 * sqrt 3 = 1558.8 and 3 sqrt 3 * sqrt 3 = 9

Answer 25

I would not change the answer to decimals, as that is not an exact answer

you should get
\[s^2= 100 \sqrt{3} \]

Answer 26

ohh ok

Answer 27

now take the square root of both sides

Answer 28

btw,
\[ \sqrt{\sqrt{x}} = \sqrt[4]{x} \]

Answer 29

I think I just confused myself. lol so I would take the square root of 100 sqrt 3?

Answer 30

and s^2 on the other side

Answer 31

10^4√3 ?

Answer 32

yes, and now you can give the decimal approximation
\[ s= 10 \sqrt[4]{3} \approx 13.161\]

Answer 33

yay!

Answer 34

btw, could also write it as
\[s= 10 \cdot 3^{\frac{1}{4}} \]
that is 3 to the 1/4 power

Answer 35

oh ok

Answer 36

Thanks for your help! That made understand it alot better.

Answer 37

made me^

Answer 38

If you could google for the formula, you could have figured it out.
divide the hexagon into 6 congruent triangles, and figure out the area of one of the triangles. then multiply by 6 to get the hexagon

Answer 39

oh ok. google just looked real confusing when I first saw the formula, but that makes more sense now.