What is the area of the polygon?

The trick here is to subdivide this polygon into smaller polygons whose areas are easier to find.  To help you get started:

Consider drawing a vertical line thru x=-1.  Then you'll have a trapezoid on the left of this vertical line.  The area of a trapezoid is

 l1 + l2                                             5+3
* 5.  More specifically, A = * 5 = 4*5 = 20 square units.  
     2                                                  2

On the right side you'll see 2 triangles:  One has a height of 4 and a base of 2.  The other has a height of 4 and a base of 3.  Area of a triangle is (1/2)(base)(height).

Sum up the areas of these three subareas of the original figure.