1. **Problem statement:** We need to find the area of a rhombus given the lengths of its diagonals, which are 9.2 cm and 7.5 cm. 2. **Formula:** The area $A$ of a rhombus can be calculated using the formula: $$A = \frac{d_1 \times d_2}{2}$$ where $d_1$ and $d_2$ are the lengths of the diagonals. 3. **Explanation:** The diagonals of a rhombus bisect each other at right angles, so the area is half the product of the diagonals. 4. **Calculation:** Substitute the given values: $$A = \frac{9.2 \times 7.5}{2}$$ 5. Multiply the diagonals: $$9.2 \times 7.5 = 69$$ 6. Divide by 2: $$A = \frac{69}{2} = 34.5$$ 7. **Final answer:** The area of the rhombus is $34.5$ square centimeters.