1. **State the problem:** We need to find the area of a compound shape made of a rectangle and a right-angled trapezoid and check if Rio's answer of 4.42 cm² is correct. 2. **Convert all measurements to centimeters:** - Height of rectangle = 19 mm = 1.9 cm - Width of top side (rectangle width) = 26 mm = 2.6 cm - Height of trapezoid slant side = 9 mm = 0.9 cm - Bottom width of trapezoid = 12 mm = 1.2 cm 3. **Calculate the area of the rectangle:** $$\text{Area}_{rectangle} = \text{height} \times \text{width} = 1.9 \times 2.6 = 4.94\, \text{cm}^2$$ 4. **Calculate the height of the trapezoid:** Since the trapezoid is right-angled, the height is the slant height = 0.9 cm. 5. **Calculate the top width of the trapezoid:** The top width of trapezoid = total top width - bottom width of trapezoid = 2.6 cm - 1.2 cm = 1.4 cm 6. **Calculate the area of the trapezoid:** Formula for trapezoid area: $$\text{Area}_{trapezoid} = \frac{(a + b)}{2} \times h$$ where $a$ and $b$ are the parallel sides, $h$ is the height. Here, $$a = 1.4, \quad b = 1.2, \quad h = 0.9$$ Calculate: $$\text{Area}_{trapezoid} = \frac{(1.4 + 1.2)}{2} \times 0.9 = \frac{2.6}{2} \times 0.9 = 1.3 \times 0.9 = 1.17\, \text{cm}^2$$ 7. **Calculate total area:** $$\text{Total area} = \text{Area}_{rectangle} + \text{Area}_{trapezoid} = 4.94 + 1.17 = 6.11\, \text{cm}^2$$ 8. **Compare with Rio's answer:** Rio's answer is 4.42 cm², which is less than the calculated 6.11 cm². **Conclusion:** Rio's answer is incorrect. The correct area of the compound shape is $6.11\, \text{cm}^2$.