Python: find area of polygon from xyz coordinates

Question

I\'m trying to use the shapely.geometry.Polygon module to find the area of polygons but it performs all calculations on the xy plane. This is fine

Answer 1

Fyi, here is the same algorithm in Mathematica, with a baby unit test

ClearAll[vertexPairs, testPoly, area3D, planeUnitNormal, pairwise];
pairwise[list_, fn_] := MapThread[fn, {Drop[list, -1], Drop[list, 1]}];
vertexPairs[Polygon[{points___}]] := Append[{points}, First[{points}]];
testPoly = Polygon[{{20, -30, 0}, {40, -30, 0}, {40, -30, 20}, {20, -30, 20}}];
planeUnitNormal[Polygon[{points___}]] :=
  With[{ps = Take[{points}, 3]},
   With[{p0 = First[ps]},
    With[{qs = (# - p0) & /@ Rest[ps]},
     Normalize[Cross @@ qs]]]];
area3D[p : Polygon[{polys___}]] :=
  With[{n = planeUnitNormal[p], vs = vertexPairs[p]},
   With[{areas = (Dot[n, #]) & /@ pairwise[vs, Cross]},
    Plus @@ areas/2]];
area3D[testPoly]