1. **State the problem:** Calculate the volume of a trapezoidal prism with given dimensions: height of vertical face = 20 cm, base length = 45 cm, base depth = 17 cm, slant height = 18 cm. 2. **Understand the shape:** The prism has a trapezoidal cross-section. The volume of a prism is given by: $$\text{Volume} = \text{Area of cross-section} \times \text{length (depth)}$$ 3. **Identify the trapezoid dimensions:** The trapezoid has two parallel sides: one vertical edge = 20 cm and the slant edge = 18 cm. The distance between these parallel sides (height of trapezoid) is 17 cm (depth). 4. **Calculate the area of trapezoid cross-section:** Formula for trapezoid area: $$\text{Area} = \frac{(a + b)}{2} \times h$$ where $a=20$, $b=18$, and $h=17$. Calculate: $$\text{Area} = \frac{(20 + 18)}{2} \times 17 = \frac{38}{2} \times 17 = 19 \times 17 = 323$$ 5. **Calculate volume:** The length of the prism (base length) is 45 cm. $$\text{Volume} = \text{Area} \times \text{length} = 323 \times 45 = 14535$$ 6. **Final answer:** $$\boxed{14535 \text{ cubic centimeters}}$$ **Note:** Your original calculation added volumes of two rectangular prisms, which is incorrect because the cross-section is trapezoidal, not rectangular. You must find the trapezoid area first, then multiply by the length.