## ganeshie8 one year ago 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

1. ganeshie8

sorry i think the polygon needs to be convex, try this |dw:1435488165543:dw|

2. ikram002p

|dw:1435488883158:dw|

3. ganeshie8

what are g and r ?

4. ikram002p

green and red

5. ganeshie8

okay

6. ikram002p

my intention was to divide any polygon to triangles idk if i make sense but i might have something to do with it

7. geerky42

*

8. 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"

9. ikram002p

|dw:1435492530592:dw|

10. ikram002p

|dw:1435492795920:dw|

11. ikram002p

Area=1/2(x1)*y2

12. ikram002p

-.-

13. ikram002p

well we need to show its correct for right triangle first xD

14. ikram002p

|dw:1435493122358:dw| the area of the triangle DEF=1/2 (area of the rectangle)

15. ganeshie8

|dw:1435493472081:dw|

16. ikram002p

without coordinate

17. ganeshie8

select and delete it

18. 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|