1. **State the problem:** We have a composite figure made of a parallelogram, a trapezoid, and a triangle with given dimensions. We need to find: - The combined area of the parallelogram and the triangle. - The total area of the composite figure. 2. **Recall formulas:** - Area of a parallelogram: $$\text{Area} = \text{base} \times \text{height}$$ - Area of a triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ - Area of a trapezoid: $$\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$$ 3. **Calculate the area of the parallelogram:** Given base = 8 cm, height = 2.5 cm $$\text{Area}_{\text{parallelogram}} = 8 \times 2.5 = 20$$ 4. **Calculate the area of the triangle:** The triangle's base is 2.5 cm (same as parallelogram height), and its height is 6 cm (same as trapezoid height). $$\text{Area}_{\text{triangle}} = \frac{1}{2} \times 2.5 \times 6 = \frac{1}{2} \times 15 = 7.5$$ 5. **Combined area of parallelogram and triangle:** $$20 + 7.5 = 27.5$$ Since the options do not include 27.5, check if the triangle height is correct. The problem states the triangle height is integral to the trapezoid, so 6 cm is correct. 6. **Calculate the area of the trapezoid:** Top base = 4 cm, bottom base = 8 cm (same as parallelogram base), height = 6 cm $$\text{Area}_{\text{trapezoid}} = \frac{1}{2} \times (4 + 8) \times 6 = \frac{1}{2} \times 12 \times 6 = 36$$ 7. **Calculate total area of composite figure:** $$20 + 7.5 + 36 = 63.5$$ **Final answers:** - Combined area of parallelogram and triangle: 27.5 cm² (closest to option B: 30 cm²) - Total area of composite figure: 63.5 cm²