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I am having trouble computing the area of the following polygon. I have the following polygon:

polygon = Polygon[{{0, 0}, {0, 1}, {2/10, 1}, {2/10, 8/10}, {4/10, 8/10}, {4/10, 6/10}, {1, 0}}]

The command

Region[polygon]

plots it just fine. I cannot hower compute its area using

RegionMeasure[polygon]

I get the following error

RegionMeasure::nmet: Unable to compute the measure of region Polygon[{{0,0},{0,1},{1/5,1},{1/5,4/5},{2/5,4/5},{2/5,3/5},{1,0}}]

It is not clear to me what causes this error.

EDIT: I need an exact result.

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    $\begingroup$ Hm. Runs without problems in version 12.0 for macos... But earlier versions of Mathematica (like 10.x and 11.x) might have had problems with Region-related functions... $\endgroup$ – Henrik Schumacher Nov 25 '19 at 16:22
  • $\begingroup$ Runs without problems in MMA version 12.0 for Windows 10 Home 64 bit. $\endgroup$ – Mariusz Iwaniuk Nov 25 '19 at 16:41
  • $\begingroup$ I don't have an older version of MMA to try it with, but you might be able to try Area[Region[polygon]] or RegionMeasure[Region[polygon]]. $\endgroup$ – MassDefect Nov 25 '19 at 18:13
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    $\begingroup$ You can always use the shoelace method for computing the area, of course. $\endgroup$ – J. M.'s technical difficulties Nov 26 '19 at 6:03
  • $\begingroup$ Thanks, indeed my version 12.0 works. Unfortunately, my server runs 11.3 which would be great to use to speed up the computation. Both Area[Region[polygon]] and RegionMeasure[Region[polygon]] do not seem to work for me. $\endgroup$ – CookieMaster Nov 26 '19 at 8:45
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If we first use DiscretizeRegion, then it's no problem on version 10.1.

RegionMeasure@DiscretizeRegion@polygon

0.54

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  • $\begingroup$ As far as I understand the DiscretizeRegion method I cannot be sure that it gives me an exact results, although it is the case here(represented as float). Unfortunately I need an exact results. $\endgroup$ – CookieMaster Nov 26 '19 at 8:41

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