Bug introduced in 11.1 or earlier and persisting through 11.2.0 or later

I use Area function to evaluate the area of the polygon. I found that when two vertex points are the same, the Area give the wrong result. For example, I define the following function:

areacoor[x_, y_] := Area@Polygon[{{x, y}, {0.5, 0.5}, {1, 1}}]

which is the area of the triangle whose vertex points is {x, y}, {0.5, 0.5} and {1, 1}. When $(x,y)$ move towards to any two other points, for example, $(x,y)\to (0.5,0.5)$, the area of the triangle will become smaller and smaller. When $(x,y)=(0.5,0.5)$, the triangle will become a line and the area should be 0. However areacoor[0.5,0.5] gives 0.707107. I wonder why I obtain this result, which I think is not reasonable.

  • 1
    $\begingroup$ I think this is a bug. Maybe somebody tried to make the definition of Area rebust for degenerating polygons, deleted duplicate vertex coordinates and somewhat mixed up Area and RegionMeasure... $\endgroup$ Jan 26, 2018 at 9:10
  • $\begingroup$ Added the bugs tag. Please report it to the tech support. $\endgroup$ Jan 26, 2018 at 11:32
  • $\begingroup$ Area[Polygon[{{0.4, 0.4}, {0.5, 0.5}, {1, 1}}]], too, misfires. $\endgroup$
    – Michael E2
    Jan 26, 2018 at 14:20
  • $\begingroup$ in 11.1 other colinear point sets generate an (incomprehensible) error message. Only a "wrong" result for coincident points. $\endgroup$
    – george2079
    Jan 26, 2018 at 16:03

1 Answer 1


Interesting question! Workaround with Evaluate works as expected:

areacoor[x_ , y_ ] :=Evaluate@Area@Polygon[{{x, y}, {0.5, 0.5}, {1, 1}}]     
areacoor[0.5, 0.5 ] 
(* 0 *)
Plot3D [areacoor[x, y], {x, 0, 1}, {y, 0, 1}]

enter image description here

appendix Without Evaluate the bug(comment @Henrik Schumacher) can be illustrated

Plot3D [Area[Polygon[{{x, y}, {1/2, 1/2}, {1, 1}}] ], {x, 0, 1}, {y,0, 1}]

enter image description here


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