# Unable to compute the area of a polygon

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 technical difficulties Nov 26 '19 at 6:03
• 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 8:45

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