What is the area of this polygon?

The area of the polygon is the number of little squares that fit into the polygon.

We can split the polygon up like this:

area of polygon  =  area of rectangle + area of triangle

area of rectangle  =  base * height

area of rectangle  =  9 * 2

area of rectangle  =  18        (You can count the squares to get the same answer.)

area of triangle  =  (1/2) * base * height

area of triangle  =  (1/2) * 9 * 6

area of triangle  =  27

area of polygon  =  area of rectangle + area of triangle

area of polygon  =  18 + 27

area of polygon  =  45

There are  45  square units in the polygon.