1. **State the problem:** We need to find the area of a rhombus with one diagonal measuring 16 cm and each side measuring 15.5 cm. 2. **Recall the formula for the area of a rhombus:** The area $A$ can be found using the formula $$A = \frac{1}{2} d_1 d_2$$ where $d_1$ and $d_2$ are the lengths of the diagonals. 3. **Identify known values:** We know one diagonal $d_1 = 16$ cm and the side length $s = 15.5$ cm. We need to find the other diagonal $d_2$. 4. **Use the properties of a rhombus:** The diagonals of a rhombus bisect each other at right angles. So, half of each diagonal forms a right triangle with the side as the hypotenuse. 5. **Set up the right triangle:** Let half of the unknown diagonal be $\frac{d_2}{2} = x$. Half of the known diagonal is $\frac{16}{2} = 8$ cm. Using the Pythagorean theorem: $$s^2 = 8^2 + x^2$$ $$15.5^2 = 64 + x^2$$ 6. **Calculate $x^2$:** $$x^2 = 15.5^2 - 64 = 240.25 - 64 = 176.25$$ 7. **Find $x$:** $$x = \sqrt{176.25} = 13.27 \text{ cm (approx)}$$ 8. **Find the full diagonal $d_2$:** $$d_2 = 2x = 2 \times 13.27 = 26.54 \text{ cm (approx)}$$ 9. **Calculate the area:** $$A = \frac{1}{2} \times 16 \times 26.54 = 8 \times 26.54 = 212.32 \text{ cm}^2$$ 10. **Compare with given options:** The closest option is 248 cm², but our calculation is approximately 212.32 cm², so none exactly match. However, the method and calculation are correct based on given data. **Final answer:** Approximately $212.32$ cm².