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

Hans007
Feb 7, 2018

#1**+1 **

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

CPhill
Feb 8, 2018