anonymous
  • anonymous
Geometry and Ratio problem!!! Help!!!
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
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.
anonymous
  • anonymous
|dw:1327787358619:dw|
Hero
  • Hero
All you do is find the areas and put them in fraction form

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More answers

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

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