Tricky Tipping Problem; 11 sided figure

[tachu101]

Homework Statement

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.

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 don't 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.

 

[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.