coordinates problem

You can split this into smaller parts and calculate the area, or use the Shoelace Theorem. Since I can't demonstrate splitting the shape here, I can use the shoelace theorem. 

Either way will give you 87/2 .

Thx, Firebolt....here's another way with something known as Pick's Theorem

Lattice points =  points with integer coordinates

Area = [  lattice points in the interior of the  figure ]  + [ lattice points on the  boundary  / 2 ]    - 1

So we have

50  +  16/2   -  1   =

50  + 8  -  1   =

57