1. The problem asks to find the area of a square with side length $9x$ centimeters. 2. The formula for the area of a square is: $$\text{Area} = \text{side}^2$$ 3. Substitute the side length $9x$ into the formula: $$\text{Area} = (9x)^2$$ 4. Simplify the expression: $$\text{Area} = 9^2 \times x^2 = 81x^2$$ 5. Therefore, the area of the square is $81x^2$ square centimeters. 6. Among the answer choices, $81x^2$ sq cm is the correct one.