1. **State the problem:** We have an 8-sided shape ABCDEFGH with given side lengths and height. We know the total area is 434 cm². We want to find the length of side CD. 2. **Identify the shape parts:** The shape has sides HG = 28 cm (bottom base), AH = FG = 12 cm (vertical sides), AB = EF = 5 cm (top and middle horizontal segments). The height of the shape (distance between HG and CD) is 20 cm. 3. **Set variables:** Let the length of CD be $x$ cm. 4. **Analyze the shape area:** The shape can be split into three parts stacked vertically: - Bottom rectangle with base HG = 28 cm and height 12 cm (from HG up to FG/AH) - Middle part between FG/AH and CD with height 8 cm (since total height 20 cm minus 12 cm) - The middle part has parallel sides CD and AB, so it forms a trapezium with height 8 cm and bases $x$ (CD) and 5 cm (AB) 5. **Calculate the areas of parts:** - Bottom rectangle area = base × height = $28 \times 12 = 336$ cm² - Middle trapezium area = $\frac{1}{2} \times (x + 5) \times 8 = 4(x + 5)$ cm² 6. **Sum of areas equals total area:** $$336 + 4(x + 5) = 434$$ 7. **Solve for $x$:** $$336 + 4x + 20 = 434$$ $$4x + 356 = 434$$ $$4x = 434 - 356 = 78$$ $$x = \frac{78}{4} = 19.5$$ 8. **Answer:** The length of CD is $\boxed{19.5}$ cm.