Unable to compute the area of a polygon

Question

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.

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... — Henrik Schumacher, Nov 25 '19 at 16:22
Runs without problems in MMA version 12.0 for Windows 10 Home 64 bit. — Mariusz Iwaniuk, Nov 25 '19 at 16:41
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]]. — MassDefect, Nov 25 '19 at 18:13
You can always use the shoelace method for computing the area, of course. — J. M.'s missing motivation, Nov 26 '19 at 06:03
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. — CookieMaster, Nov 26 '19 at 08:45
You could always try CloudEvaluate[Area[polygon]] in your 11.3 session. I believe it will use the most recent version in the cloud. — Greg Hurst, Nov 26 '19 at 12:37

score 2 · Accepted Answer · answered Nov 25 '19 at 22:18

2

If we first use DiscretizeRegion, then it's no problem on version 10.1.

RegionMeasure@DiscretizeRegion@polygon

0.54

answered Nov 25 '19 at 22:18

NonDairyNeutrino

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. – CookieMaster Nov 26 '19 at 08:41

1 Answers1