1. Joined
    11 Nov '05
    Moves
    43938
    20 Feb '07 21:201 edit
    Originally posted by GinoJ
    Hey Fabian, life too short to get angry brotha'.
    No no, I'm not angry - if you just tell me the glitch?

    If I ask you the same question to you, but now with the Area of a regular heptagon with each side being 1 cm in length, what will be your answer?

    This one is exclusively for Gino. Just so he might show off and prove that he knows what he's talking about. Do you have enough math, Gino?
  2. Joined
    20 Jan '07
    Moves
    1005
    21 Feb '07 05:111 edit
    Originally posted by FabianFnas
    No no, I'm not angry - if you just tell me the glitch?

    If I ask you the same question to you, but now with the Area of a regular heptagon with each side being 1 cm in length, what will be your answer?

    This one is exclusively for Gino. Just so he might show off and prove that he knows what he's talking about. Do you have enough math, Gino?
    I do not think I could ever have as much as yours. 😉

    [edit] So, I leave the "posers and puzzles" section to your dominance since I am just an ignorant. 😠

    Have fun!
  3. Joined
    11 Nov '05
    Moves
    43938
    21 Feb '07 07:06
    Originally posted by GinoJ
    I do not think I could ever have as much as yours. 😉

    [edit] So, I leave the "posers and puzzles" section to your dominance since I am just an ignorant. 😠

    Have fun!
    If you leave, Gino, much of the recent fun goes with you.
    This fourm is very dependant of people who invent or copy problems so the rest of us put the little grey ones in ction.

    One problem is better than no problem, even if a good problem is better than an ordinary one. And favorites is always welcome if they're good.

    The way of solving the heptagon problem could be very like that of the hexagon. Give it a try and see where it leads.
  4. Joined
    15 Feb '07
    Moves
    667
    21 Feb '07 07:39
    A heptagon has 7 sides, does it not? I daresay the answer to your query will end up a great deal more complicated than the previous question, because it will involve trigonometry, and the sines and cosines of angles which have no exact answer, only approximations.

    With a hexagon, you were dealing with sin(60d) which is very well known as an exact number (sqrt(3)/2)

    The area of a heptagon would be 3.5 * sin(64+2/7d).
  5. Joined
    07 Sep '05
    Moves
    35068
    21 Feb '07 12:581 edit
    It's not too hard to extend it to a regular polygon with n sides (for n > 2).

    You can break it down into n isosceles triangles with a base or length 1 and a height of 1/[2tan(180/n)]

    So the area = n/[4tan(180/n)]

    (As a check, put in n = 4 and you get A = 1 as expected)
  6. Subscribersonhouse
    Fast and Curious
    slatington, pa, usa
    Joined
    28 Dec '04
    Moves
    53223
    21 Feb '07 18:161 edit
    Since a regular hexagon is composed of 6 equalateral triangles you can just solve for the area of one triangle and multiply by 6:
    A=Sqr root of (S*(S-a)*(S-b)*(S-c)
    a, b and c all = exactly 1.
    S= (a+b+c)/2
    S= 3/2
    S= 1.5
    So, Sqr root of (1.5)*(0.5)*(0.5)*(0.5) = Sqr root (1.5)*(0.125)
    = Sqr root of (0.1875) or 0.433012702 = area of equalateral triangle of side 1.
    0.433012702 * 6= 2.598076211 Square units= area of regular hexagon with unit sides. So 2.59 and change is the answer.
    I deliberately did it a differant way from Fabian and got exactly the same answer so what is wrong with YOUR logic?
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