The overall rectangle is 5' by 12', so 60 ft².
The rectangular cutout is 2' by 3', so 6 ft².
The triangular cutout has a 3' base and a 4' height, so is 6 ft².
The green area is 60 ft² - 6 ft² - 6 ft² = 48 ft².
You need 48 square feet of outdoor carpet for this green in your putt-putt golf course.