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i would like to ask a question

if we have some parametric plot and it will be a shape, can we use "area" function to calculate that shape?

Here is the simple program

\[Alpha] = \[Pi];
\[Alpha]1 = .5 \[Pi];
g[1] = ParametricPlot[{-8 + u Cos[\[Alpha]1], 
    u Sin[\[Alpha]1]}, {u, -8, 8}, PlotStyle -> Green];
g[2] = ParametricPlot[{u Cos[\[Alpha]], 8 + u Sin[\[Alpha]]}, {u, -8, 
    8}, PlotStyle -> Green];
g[3] = ParametricPlot[{8 + u Cos[\[Alpha]1], 
    u Sin[\[Alpha]1]}, {u, -8, 8}, PlotStyle -> Green];
g[4] = ParametricPlot[{u Cos[\[Alpha]], -8 + u Sin[\[Alpha]]}, {u, -8,
     8}, PlotStyle -> Green];
ar = {};
AppendTo[gar, g[1]];
AppendTo[gar, g[2]];
AppendTo[gar, g[3]];
AppendTo[gar, g[4]];
Show[gar, AxesOrigin -> {0, 0}, PlotRange -> All]

enter image description here

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Show[gar, AxesOrigin -> {0, 0}, PlotRange -> All] //BoundaryDiscretizeGraphics // Area

256

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  • $\begingroup$ its not working, i receive the this error BoundaryMeshRegion::buncl: At least one boundary was not closed in BoundaryMeshRegion[{{-8.,-8.},{-8.,-7.84297},{-8.,-7.68594},{-8.,-7.34547},{-8.,-7.02755},{-8.,-6.71588},{-8.,-6.37778},<<37>>,{-8.,6.02834},{-8.,6.36812},{-8.,6.68533},{-8.,6.99632},{-8.,7.16501},{-8.,7.33371},<<162>>},{{},{Line[{<<1>>}]}}]. >> $\endgroup$
    – 葉柏樂
    Oct 14, 2022 at 6:05
  • $\begingroup$ @葉柏樂AbdullahSyafiq Or DiscretizeGraphics /@ {g[1], g[2], g[3], g[4]} // RegionUnion // Show // BoundaryDiscretizeGraphics // Area $\endgroup$
    – cvgmt
    Oct 14, 2022 at 6:43
  • $\begingroup$ i dont know why, it still not work in that program $\endgroup$
    – 葉柏樂
    Oct 14, 2022 at 7:18
  • $\begingroup$ @葉柏樂AbdullahSyafiq version 13.1 $\endgroup$
    – cvgmt
    Oct 14, 2022 at 7:21
  • $\begingroup$ maybe because i still use version 10.0 $\endgroup$
    – 葉柏樂
    Oct 14, 2022 at 7:24

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