Posers and Puzzles

Posers and Puzzles

  1. Joined
    20 Jan '07
    Moves
    1005
    20 Feb '07 19:41
    One of the sides of a regular hexagon is 1cm. Find the area of the hexagon.

    Show your work.
  2. Joined
    11 Nov '05
    Moves
    43938
    20 Feb '07 19:58
    Originally posted by GinoJ
    One of the sides of a regular hexagon is 1cm. Find the area of the hexagon.

    Show your work.
    A regular hexagon with each side = 1 cm consist of 6 equilateral triangles with sides 1 cm. Each triangle have an area of sqrt(3)/4 = 0.43 giving the hexagon an area of 6 * sqrt(3)/4 = 2.60

    Near enough?
  3. Joined
    20 Jan '07
    Moves
    1005
    20 Feb '07 20:051 edit
    Originally posted by FabianFnas
    A regular hexagon with each side = 1 cm consist of 6 equilateral triangles with sides 1 cm. Each triangle have an area of sqrt(3)/4 = 0.43 giving the hexagon an area of 6 * sqrt(3)/4 = 2.60

    Near enough?
    The answer is a "natural number" if I must give a clue. [edit]Il also has an extremely short solution.
  4. Joined
    12 Mar '03
    Moves
    37893
    20 Feb '07 20:16
    Really? 'Natural' as in 'Positive Integer'? Are we that close to a revolution in euclidian geometry then?
  5. Joined
    20 Jan '07
    Moves
    1005
    20 Feb '07 20:171 edit
    Originally posted by Mephisto2
    Really? 'Natural' as in 'Positive Integer'? Are we that close to a revolution in euclidian geometry then?
    0,1,2,3,4,5,6,7,8,9 etc...


    [edit] Eliminate 0. 😛

    So, another clue: It's a positive integer.
  6. Joined
    12 Mar '03
    Moves
    37893
    20 Feb '07 20:26
    The very simple solution is expressed as a positive integer number of cm²?
  7. Standard memberPBE6
    Bananarama
    False berry
    Joined
    14 Feb '04
    Moves
    28719
    20 Feb '07 20:281 edit
    Originally posted by GinoJ
    0,1,2,3,4,5,6,7,8,9 etc...


    [edit] Eliminate 0. 😛

    So, another clue: It's a positive integer.
    There's no chance it's a positive integer. The area is (3/2)*SQRT(3), as reported (rounded) above. No matter how many times you multiply an irrational number by a rational one (other than 0 of course), you'll never get a positive integer.
  8. Joined
    20 Jan '07
    Moves
    1005
    20 Feb '07 20:332 edits
    La solution est:

    1.5a
    a*a=3
  9. Sigulda, Latvia
    Joined
    30 Aug '06
    Moves
    4048
    20 Feb '07 20:411 edit
    Originally posted by FabianFnas
    A regular hexagon with each side = 1 cm consist of 6 equilateral triangles with sides 1 cm. Each triangle have an area of sqrt(3)/4 = 0.43 giving the hexagon an area of 6 * sqrt(3)/4 = 2.60

    Near enough?
    This is correct, I'm not quite sure why GinoJ thinks that it's not. Perhaps, Gino, you can show us your idea? According to what I'm learning at school, Fabian gave a fully correct answer. That is the way how this exercise should be solved. Perhaps you didn't mean a hexagon but a polygon with different number of sides.
  10. Joined
    12 Mar '03
    Moves
    37893
    20 Feb '07 20:46
    Originally posted by GinoJ
    OK, then.

    [edit]

    1.5a
    a*a=3
    So, '1.5a' is a positive integer a.k.a. 'natural number'? You make me feel sorry about myself to even want to read this forum anymore.
  11. Joined
    20 Jan '07
    Moves
    1005
    20 Feb '07 20:46
    Originally posted by kbaumen
    This is correct, I'm not quite sure why GinoJ thinks that it's not. Perhaps, Gino, you can show us your idea? According to what I'm learning at school, Fabian gave a fully correct answer. That is the way how this exercise should be solved. Perhaps you didn't mean a hexagon but a polygon with different number of sides.
    Are you blind?
  12. Joined
    20 Jan '07
    Moves
    1005
    20 Feb '07 20:47
    Originally posted by Mephisto2
    So, '1.5a' is a positive integer a.k.a. 'natural number'? You make me feel sorry about myself to even want to read this forum anymore.
    I was tricking you guys. 😀
  13. Joined
    11 Nov '05
    Moves
    43938
    20 Feb '07 21:03
    Originally posted by GinoJ
    I was tricking you guys. 😀
    Don't try, Gino, Explain your natural answer, or what your flaw in your reasoning...

    Don't "I was tricking you" me... 😠
  14. Joined
    20 Jan '07
    Moves
    1005
    20 Feb '07 21:05
    Originally posted by FabianFnas
    Don't try, Gino, Explain your natural answer, or what your flaw in your reasoning...

    Don't "I was tricking you" me... 😠
    Ok, sire.
  15. Joined
    20 Jan '07
    Moves
    1005
    20 Feb '07 21:103 edits
    Hey Fabian, thank God I am bein' soft G.
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