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Find the area of the quadrilateral formed with vertices at point (1,2) (5,8) (8,6) (4,0)

Hans007  Feb 7, 2018
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We can do this with something known as "Pick's Theorem"

 

Here's a pic  :

 

 

Area  =

 

Number of Interior Lattice Points  + Number of Border Lattice Points / 2   - 1

 

Where a "lattice point"  is a point with integer coordinates  [ in our case....the intersection of two gridlines]

 

Number of interior Lattice Points  = 24

 

Number of Border Lattice Points  =  6

 

So....the area is

 

24  +  6/2  + 1   =

 

24 + 3  - 1  =

 

26 units^2

 

 

cool cool cool

CPhill  Feb 8, 2018

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