Iregular polygon-area

[GABRIELSAS]

Hi,

How can I determine the area and center of mass of a polygon knowing the coordinates of its points? the lenght of the segment 01 and the angle between lines 05 and 45?

Thank you,

Gabriel

[Werner_E]

Here is the sheet. I simplified the routines in my first sheet (in fact I deleted them as we won't need them) so the creation of the polygon is done only once.

As of the differences with your Autocad sheet there might be an error somewhere - probably for positive alpha, but I can't think of where. So handle with case and double check.

[GABRIELSAS]

Thank you Werner. Much appreciated!

[Werner_E]

You are welcome!

The areas you calculated with Autocad are definitely wrong for positive values of alpha.

The area is easily calculated with 7/8*B(alpha)*5.5 and Autocad gives you B(20°)=3,97 which would yield an area of 19.106 and not 18.63.

The smallest area possible is when 05 and 45 are at right angles, that is when alpha = 90°-beta=24,347° and that area is 19.073. There is no area smaller possible.

Could it be that Autocad gives you an oriented area so that areas above and below y=0 partially cancel? This would be an explanation why we don't see any discrepancy for negative alpha. But then I would wonder what figure the center of gravity is calculated for in Autocad.

P.S.: I added a grid in the drawing as it seemed to me that for larger positive alphas I am not seeing the 3:1 spacing - fortunately that was an optical illusion.

[GABRIELSAS]

Hi Werner,

Two reasons I found for the difference in areas. In autocad I used 65 degrees while in mathcad is 65.643. Second, I drew the sections in autocad with one decimal. When I use all digits the results are identical .

Problem solved! Thank again and have a nice weekend.

/gabriel