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Would you please explain to me a way that I can divide a polygon by means of a special line "represents the zero axis" into two regions so that I can determine each region individually. The question of : How to check if a line segment intersects with a polygon? is a nice example, however, I couldn't find a correct way to separate both upper and lower sub-polygons individually, and hence I can find the Area for each of them.

enter image description here

The data input are same for the mentioned question:

list = {{4.4, 14}, {6.7, 15.25}, {6.9, 12.8}, {9.5, 14.9}, {13.2, 
11.9}, {10.3, 12.3}, {6.8, 9.5}, {13.3, 7.7}, {0.6, 1.1}, {1.3, 
2.4}, {2.45, 4.7}};
Graphics[{Red, Line[{{0, 10}, {20, 0}}], Black, Polygon[list]}]
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    $\begingroup$ I have not tested this, but have you tried HalfPlane and RegionIntersection (potentially followed by another discretization step)? $\endgroup$
    – Szabolcs
    Apr 25, 2017 at 7:49
  • $\begingroup$ @Kuba The inputs and outputs are same for this example:mathematica.stackexchange.com/questions/66152/… $\endgroup$
    – Mehmet
    Apr 25, 2017 at 8:03
  • $\begingroup$ @Szabolcs, I tried to use the mentioned commands but RegionIntersection probably needs same number of Points? $\endgroup$
    – Mehmet
    Apr 25, 2017 at 8:06
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    $\begingroup$ I am not sure what you mean by "needs same number of Points", but what have you tried exactly? It works for me. Did you look up HalfPlane and RegionIntersection in the documentation? $\endgroup$
    – Szabolcs
    Apr 25, 2017 at 9:07

2 Answers 2

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Following Szabolcs' suggestion,

Graphics[{Red, HalfPlane[{{0, 10}, {20, 0}}, {0, 1}], Black, Polygon[list]}]

graphics

Then direct applying RegionIntersection gives what you need:

Graphics[{RegionIntersection[HalfPlane[{{0, 10}, {20, 0}}, {0, 1}], Polygon[list]]}]

output

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In:

xss = {{4.4, 14}, {6.7, 15.25}, {6.9, 12.8}, {9.5, 14.9}, {13.2, 
    11.9}, {10.3, 12.3}, {6.8, 9.5}, {13.3, 7.7}, {0.6, 1.1}, {1.3, 
    2.4}, {2.45, 4.7}};
halfPlane[y_] := HalfPlane[{{0, 10}, {20, 0}}, {0, y}];
halfRegion[reg1_, reg2_] := 
 DiscretizeRegion[RegionIntersection[reg1, reg2], AspectRatio -> 1]
halfRegion[Polygon[xss], halfPlane[#]] & /@ {-1, 1}

Out: enter image description here

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