+130110 We can use something known as Pick's Theorem here
The black points are known as lattice points
Area = interior lattice points + boundary lattice points /2 -1
First figure
Interior lattice points = 6
Boundary lattice points = 6
Area = 6 + 6/2 -1 = 6 + 3 - 1 = 8
Second figure
Interior lattice points = 3
Boundary lattice points = 5
Area = 3 + 5/2 - 1 = 3 + 3/2 = 4.5
