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

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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
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sorry i think the polygon needs to be convex, try this |dw:1435488165543:dw|
|dw:1435488883158:dw|
what are g and r ?

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green and red
okay
my intention was to divide any polygon to triangles idk if i make sense but i might have something to do with it
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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"
|dw:1435492530592:dw|
|dw:1435492795920:dw|
Area=1/2(x1)*y2
-.-
well we need to show its correct for right triangle first xD
|dw:1435493122358:dw| the area of the triangle DEF=1/2 (area of the rectangle)
|dw:1435493472081:dw|
without coordinate
select and delete it
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|