1. **State the problem:** We need to find the total cost of sod to cover a football field shaped like a parallelogram with a base of 120 yards and a height of 53 \frac{1}{3} yards. The cost per square yard of sod is 1.35. 2. **Formula for area of a parallelogram:** $$\text{Area} = \text{base} \times \text{height}$$ 3. **Convert mixed number to improper fraction:** $$53 \frac{1}{3} = \frac{160}{3}$$ 4. **Calculate the area:** $$\text{Area} = 120 \times \frac{160}{3}$$ 5. **Simplify the multiplication:** $$= \cancel{120} \times \frac{160}{3} = \frac{\cancel{120} \times 160}{3}$$ Since 120 and 3 share a common factor 3: $$= \frac{120 \div 3 \times 160}{1} = 40 \times 160 = 6400$$ 6. **Calculate total cost:** $$\text{Total cost} = \text{Area} \times \text{cost per square yard} = 6400 \times 1.35$$ 7. **Multiply to find total cost:** $$6400 \times 1.35 = 8640$$ **Final answer:** The total cost of sod is 8640.