I'm guessing that yo're supposed to use Pick's Theorem:
Area = (Number of Interior Points) + ½·(Number of Boundary Points) - 1
For instance, in the figure at top-right, there are 3 interior points and 12 boundary points, so:
Area = (3) + ½·(12) - 1 = 3 + 6 - 1 = 8
A point is one of the coordinate points on the graph paper.
An interior point is one of these points found inside the figure.
A boundary point is any point that is on the edge of the figure.
For the bottom-right figure, there are 8 interior points and 4 boundary points:
Area = 8 + ½·4 - 1 = 9
Assuming that each square is one unit, the first one is \(2*1+5*2+1*1=13\) units
2. This is two equal triangles. So \((4*2)/2+(4*2)/2\)=4
3. There are two pentagons of equal area. So the area would be \(7.5*2=15\)
4. Make a 4x5 square around it. Subtract 4 from one of the outside triangles. Subract 2 from another. Finally subtract 5 from the last. So \(20-4-5-2=9\).