We can use something called "Pick's Theorem to solve this.....
The theorem says that as long as the vertices of a figure lie on integer coordinates .....like yours....we can calculate the area as :
B/2 + I - 1
Where B is the number of boundary points [" boundary points" are defined as the number of time the edges of the figure intersect integer coordinates...i,e.....the intersection of the grid lines ]
And I is the number of interior points [ again....these are the number of interior points that lie on integer coordinates]
We have 14 boundary points and 27 interior points
So.....the area = 14/2 + 27 - 1 = 7 + 27 - 1 = 34 - 1 = 33 sq units
Heres's a pic :
