1. **Stating the problem:** We need to find the volume of a trapezoidal prism with given side lengths. 2. **Formula for volume of a prism:** The volume $V$ of a prism is given by: $$V = \text{Area of base} \times \text{height}$$ 3. **Identify the base shape and dimensions:** The base is a trapezium (trapezoid) with parallel sides $AB = 16$ cm and $EF = 14$ cm. The height of the trapezium (distance between the parallel sides) can be found using the other given lengths. 4. **Calculate the height of the trapezium:** Given $FG = 16$ cm and $GC = 13$ cm, these likely represent the legs of the trapezium or the height components. Assuming $FG$ is the height of the prism (length between the trapezium bases), and $GC$ is the height of the trapezium. 5. **Calculate the area of the trapezium base:** The area $A$ of a trapezium is: $$A = \frac{(a + b)}{2} \times h$$ where $a = 16$ cm, $b = 14$ cm, and $h = 13$ cm. Calculate: $$A = \frac{(16 + 14)}{2} \times 13 = \frac{30}{2} \times 13 = 15 \times 13 = 195 \text{ cm}^2$$ 6. **Calculate the volume of the prism:** Using the height of the prism $FG = 16$ cm: $$V = A \times \text{height} = 195 \times 16 = 3120 \text{ cm}^3$$ **Final answer:** The volume of the trapezoidal prism is $3120$ cm$^3$.