58 square units
To calculate the area of the polygon, we need to find the area of each individual shape and then add them together.
The vertical rectangular base has an area of 12 * 3 = 36 square units.
The horizontal rectangular crossbar has an area of 12 * 2 = 24 square units.
To find the total area, we add the two areas together: 36 + 24 = 60 square units.
However, we must subtract the area of the overlapping region at the top where the horizontal crossbar meets the vertical base. This region is a rectangle with an area of 4 * 2 = 8 square units.
Subtracting the overlapping region gives us: 60 - 8 = 52 square units.
Therefore, the area of the polygon is 52 square units.