Geometry and Ratio problem!!! Help!!!

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Geometry and Ratio problem!!! Help!!!

Mathematics
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The figure ABCDEF below is a regular hexagon, and point P lies on side AB, with AP=3 cm and PB=1cm. Line PE meets AD at Q. What is the ratio of the area of quadrilateral AQEF to the area of hexagon ABCDEF? Express your answer as a common fraction.
|dw:1327787358619:dw|
All you do is find the areas and put them in fraction form

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how do I find the area of AQEF?
It's not that difficult
Can you give me some hints? Please.
|dw:1327787517063:dw|
There's one hint
Ready for the next hint?
yes
Ready for the next one?
Wait, so all the side lengths are 3? Isn't it 4?
oh okay, I didn't read that in-depth. This is different
ok
|dw:1327787748238:dw|
Yes
You have to find the area of the hexagon first. There's no way to avoid that
Good luck with this
Area of the hexagon = |dw:1327788115227:dw|
I don't have a solid approach to this. Sorry bud
I can take a look at it later maybe.
Oh, ok. Thanks for trying though.
AD splits the hex into two halves. That might help.
ok, I will keep trying.
|dw:1327788413768:dw|
|dw:1327788548241:dw|
Area of hexagon equals 24sqrt{3}, so ABCD equals 12sqrt{3} and ADEF equals 12 sqrt{3} as well.
find the heigh of AE, calcuate the area of triangle APE and AFE...then you have an answer i guess
the height of AE is 4sqrt{3}, APE is 6sqrt{3}. But how do I find AFE and AQP then?
|dw:1327789175987:dw|
What about AQE?
I made an mistake, AEF should be 4sqrt{3}.
asnaseer, moneybird, and mertsj should be able to figure this out.
I think matematika and yociyoci are doing well so far...
im not sure....but isn't there formula for calulating triangle if you know one side and angels?maybe with help of this you can find out area of this one
But I don't know that formula, is there another approach?
You can find the height of triangle EDQ
triangle EDQ and triangle PAQ are similar
so the height of EDQ is|dw:1327790090893:dw| ?
AD splits the hexagon in halves so quadrilateral AQEF = quadrilateral AFED - triangle FDQ
you mean - EDQ moneybird
is triangle EDQ eqauls to 32sqrt{3}/7 ?
ya |dw:1327790174473:dw| From midpoint of ED to midpoint of AB is 4 sqrt(3)
now use ratio to find the height of triangle EDQ and triangle APQ
\[\frac{4}{h} = \frac{3}{4\sqrt{3}-h}\]
I don't quite understand what you just did. Can you clarify, please?
Which part?
the diagram
when you cut the hexagon into six equal pieces, you take out one of the piece, which is a triangle
ok
|dw:1327790925432:dw|so the area of the hexagon is 24 sqrt(3) ratio is
ok, i understand. thank you very much, guys!!!! I appreciated!!!
very well explained moneybird
ty

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