We can split up this polygon into three separate sections A, B, and C as seen in image below here.
So each "square" on grid has area of 1 square unit, so we just need to count blue square unit.
It's easy to count blue unit square on section C. That would be 10 square units.
Now section B is triangle so we can find area of triangle. We need base and height and lucky, it is right angle triangle so we just need to count unit length of base and height.
base is 4 unit long and height is 4 units high, so the area of B would be (1/2) ·4·4 = 8 square units
Now for section A, it's rectangle. We can just count length and width.
It has length 12 units and width 5 units, so the area of A would be 12·5 = 60 square units.
So the area of this polygon would be A + B + C = 60 + 8 + 10 = 78