1. **Problem Statement:** Calculate the area of a hexagonal sun deck with a top side length of 40 cm, a bottom side length of 96 cm, and a vertical height of 90 cm. 2. **Formula Used:** The area of a trapezoid (which the hexagon can be divided into) is given by: $$\text{Area} = \frac{(a + b)}{2} \times h$$ where $a$ and $b$ are the lengths of the two parallel sides, and $h$ is the height. 3. **Explanation:** The hexagon can be considered as a trapezoid with the top side $a = 40$ cm, the bottom side $b = 96$ cm, and the height $h = 90$ cm. 4. **Calculation:** $$\text{Area} = \frac{(40 + 96)}{2} \times 90 = \frac{136}{2} \times 90 = 68 \times 90 = 6120$$ 5. **Final Answer:** The area of the sun deck is $6120$ square centimeters.