To find the area of the compound figure and the missing angle 'x', we will break down the figure into simpler shapes and use trigonometric ratios. Part 1: Finding the Area of the Compound Figure We can decompose the figure into four basic shapes: three rectangles and one right-angled triangle. Step 1: Identify the shapes and their dimensions. Rectangle 1 (R1 - Bottom section): This rectangle spans the entire width of the base and has a height of 4 cm. Width = $4 \text{ cm} + 8 \text{ cm} + 6 \text{ cm} = 18 \text{ cm}$ Height = $4 \text{ cm}$ Rectangle 2 (R2 - Left section above R1): This rectangle is on the far left, above the 4 cm height of R1. Width = $4 \text{ cm}$ Height = $8 \text{ cm} - 4 \text{ cm} = 4 \text{ cm}$ (total height on left is 8 cm, 4 cm is part of R1) Rectangle 3 (R3 - Middle section above R1): This rectangle is in the middle, above the 8 cm width segment. Width = $8 \text{ cm}$ Height = $4 \text{ cm}$ Triangle 1 (T1 - Right section above R1): This is a right-angled triangle on the far right, above the 6 cm width segment. Base = $6 \text{ cm}$ Height = $4 \text{ cm}$ Step 2: Calculate the area of each individual shape. Area of R1: $$A_{R1} = \text{width} \times \text{height} = 18 \text{ cm} \times 4 \text{ cm} = 72 \text{ cm}^2$$ Area of R2: $$A_{R2} = \text{width} \times \text{height} = 4 \text{ cm} \times 4 \text{ cm} = 16 \text{ cm}^2$$ Area of R3: $$A_{R3} = \text{width} \times \text{height} = 8 \text{ cm} \times 4 \text{ cm} = 32 \text{ cm}^2$$ Area of T1: $$A_{T1} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \text{ cm} \times 4 \text{ cm} = 12 \text{ cm}^2$$ Step 3: Calculate the total area. The total area of the compound figure is the sum of the areas of these individual shapes. $$A_{\text{total}} = A_{R1} + A_{R2} + A_{R3} + A_{T1}$$ $$A_{\text{total}} = 72 \text{ cm}^2 + 16 \text{ cm}^2 + 32 \text{ cm}^2 + 12 \text{ cm}^2$$ $$A_{\text{total}} = 132 \text{ cm}^2$$ The total area of the compound figure is $\boxed{\text{132 cm}^2}$. Part 2: Finding the Missing Angle 'x' Angle 'x' is located in the right-angled triangle (T1) on the right side of the figure. Step 1: Identify the known sides relative to angle 'x'. The side opposite* to angle 'x' is the height of the triangle, which is 4 cm. The side adjacent* to angle 'x' is the base of the triangle, which is 6 cm. Step 2: Use the tangent trigonometric ratio. The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side. $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$$ $$\tan(x) = \frac{4 \text{ cm}}{6 \text{ cm}}$$ $$\tan(x) = \frac{2}{3}$$ Step 3: Calculate the angle 'x' using the inverse tangent function. $$x = \arctan\left(\frac{2}{3}\right)$$ $$x \approx 33.690067^\circ$$ Step 4: Round the angle to one decimal place. $$x \approx 33.7^\circ$$ The missing angle 'x' is $\boxed{33.7^\circ}$.