1. **State the problem:** Calculate the volume of a trapezoidal prism with the following dimensions: - One parallel side (a) = 5.2 cm - The other parallel side (b) = 9.4 cm - The height (h) of the trapezoid = 6 cm - The depth (length) of the prism (L) = 205 mm 2. **Convert all units to the same system:** Since most dimensions are in cm, convert 205 mm to cm: $$205\ \text{mm} = \frac{205}{10} = 20.5\ \text{cm}$$ 3. **Formula for the volume of a trapezoidal prism:** The volume $V$ is given by the area of the trapezoidal base times the length: $$V = A_{base} \times L$$ where the area of the trapezoid is: $$A_{base} = \frac{(a + b)}{2} \times h$$ 4. **Calculate the area of the trapezoid:** $$A_{base} = \frac{(5.2 + 9.4)}{2} \times 6 = \frac{14.6}{2} \times 6 = 7.3 \times 6 = 43.8\ \text{cm}^2$$ 5. **Calculate the volume:** $$V = 43.8 \times 20.5 = 897.9\ \text{cm}^3$$ 6. **Convert volume to dm³:** Since $1\ \text{dm}^3 = 1000\ \text{cm}^3$, divide by 1000: $$V = \frac{897.9}{1000} = 0.8979\ \text{dm}^3$$ **Final answer:** $$\boxed{0.8979\ \text{dm}^3}$$