ganeshie8
  • ganeshie8
show that \[A=i+\frac{b}{2}-1\] for a polygon with integer coordinates. \(A\) : Area of polygon \(b\) : number of lattice points on the boundary \(i\) : number of lattice points in the interior of polygon
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ganeshie8
  • ganeshie8
sorry i think the polygon needs to be convex, try this |dw:1435488165543:dw|
ikram002p
  • ikram002p
|dw:1435488883158:dw|
ganeshie8
  • ganeshie8
what are g and r ?

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ikram002p
  • ikram002p
green and red
ganeshie8
  • ganeshie8
okay
ikram002p
  • ikram002p
my intention was to divide any polygon to triangles idk if i make sense but i might have something to do with it
geerky42
  • geerky42
*
ikram002p
  • ikram002p
i have this crazy idea, 1-i'll assume any polygon could be divided into triangles 2-i'll prove that a triangle can have area of this formula 3-lets generate this for several joined triangles 4-generate to any polygon "this should end up neat"
ikram002p
  • ikram002p
|dw:1435492530592:dw|
ikram002p
  • ikram002p
|dw:1435492795920:dw|
ikram002p
  • ikram002p
Area=1/2(x1)*y2
ikram002p
  • ikram002p
-.-
ikram002p
  • ikram002p
well we need to show its correct for right triangle first xD
ikram002p
  • ikram002p
|dw:1435493122358:dw| the area of the triangle DEF=1/2 (area of the rectangle)
ganeshie8
  • ganeshie8
|dw:1435493472081:dw|
ikram002p
  • ikram002p
without coordinate
ganeshie8
  • ganeshie8
select and delete it
ikram002p
  • ikram002p
so to find the area we divide them into squares and each square being denoted by number of lattice points in the interior |dw:1435493745391:dw|