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

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