Homework Help: Tricky Tipping Problem; 11 sided figure

1. Dec 8, 2007

tachu101

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. Dec 8, 2007

Dick

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.