1. **Problem Statement:** Calculate the surface area of a trapezoidal prism with the following dimensions: - Front trapezoid bases: 10 cm and 8 cm - Height of trapezoid: 8 cm - Length of prism: 16 cm - Top trapezoid base: 6 cm - Vertical height of side trapezoid: 7 cm 2. **Formula for Surface Area of a Prism:** The surface area (SA) of a prism is the sum of the areas of all its faces: $$SA = 2 \times \text{Base Area} + \text{Perimeter of base} \times \text{Length}$$ 3. **Calculate the area of the trapezoidal base:** The area of a trapezoid is given by: $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two bases and $h$ is the height. For the front trapezoid: $$b_1 = 10, \quad b_2 = 8, \quad h = 8$$ Calculate: $$\text{Area} = \frac{(10 + 8)}{2} \times 8 = \frac{18}{2} \times 8 = 9 \times 8 = 72$$ 4. **Calculate the perimeter of the trapezoidal base:** We need the lengths of all four sides. We have two bases: 10 cm and 8 cm. Calculate the non-parallel sides (legs) using the Pythagorean theorem: The height is 8 cm, and the difference between bases is $10 - 8 = 2$ cm. Each leg length: $$\sqrt{8^2 + 1^2} = \sqrt{64 + 1} = \sqrt{65} \approx 8.06$$ So perimeter: $$P = 10 + 8 + 8.06 + 8.06 = 34.12$$ 5. **Calculate the lateral surface area:** $$\text{Lateral Surface Area} = P \times \text{Length} = 34.12 \times 16 = 545.92$$ 6. **Calculate total surface area:** $$SA = 2 \times 72 + 545.92 = 144 + 545.92 = 689.92$$ **Final answer:** $$\boxed{689.92 \text{ cm}^2}$$ This is the amount of wrapping paper needed to cover the trapezoidal prism.