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Tricky Tipping Problem; 11 sided figure

  1. Dec 8, 2007 #1
    1. The problem statement, all variables and given/known data
    A regular polygon of 11 sides is on an adjustable incline. The polygon has sides on 1.32 meters each. At what angle of the incline will the polygon tip over. Extra: what is the area of a cross section of the polygon.

    3. The attempt at a solution
    This problem has to do with center of mass. I have to calculate at what angle the center of mass will be over the 90 degree mark.

    I found that each interior angle of the 11 sided figure is 147.27 degrees. I then dont know how to explain it but I took half of that angle and ended up with 73.63 degrees. Because the center of mass has to be at a right angle to tip over I then did 90-73.63= 16.4 degrees and I think that this is my answer.

    The area of the cross section I think is 16.3 m^2 because I looked up an equation on wikipedia that said the area is equal to 9.356*(side length)^2

    Can anyone confirm this.
  2. jcsd
  3. Dec 8, 2007 #2


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    Right on both. You might try thinking about how to derive the wikipedia formula. It's not that hard. Split the polygon into 11 isosceles triangles with a vertex at the center. The central angle is 360/11. Do trig.
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