1. **State the problem:** We need to find the combined area of the parallelogram and the triangle in the composite figure. 2. **Recall formulas:** - Area of a parallelogram: $$\text{Area} = \text{base} \times \text{height}$$ - Area of a triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Calculate the area of the parallelogram:** Given base = 4 cm and height = 6 cm, $$\text{Area}_{\text{parallelogram}} = 4 \times 6 = 24$$ cm$^2$ 4. **Calculate the area of the triangle:** Given base = 8 cm and height = 2.5 cm, $$\text{Area}_{\text{triangle}} = \frac{1}{2} \times 8 \times 2.5 = \frac{1}{2} \times 20 = 10$$ cm$^2$ 5. **Find the combined area:** $$\text{Combined area} = 24 + 10 = 34$$ cm$^2$ **Final answer:** The combined area of the parallelogram and the triangle is **34 cm$^2$**. --- Since the user also asked for the area of the composite figure (parallelogram + trapezoid + triangle), we calculate that as well: 6. **Calculate the area of the trapezoid:** Given bases 8 cm and 4 cm, height 2.5 cm, $$\text{Area}_{\text{trapezoid}} = \frac{1}{2} \times (8 + 4) \times 2.5 = \frac{1}{2} \times 12 \times 2.5 = 6 \times 2.5 = 15$$ cm$^2$ 7. **Calculate total area of composite figure:** $$\text{Total area} = 24 + 10 + 15 = 49$$ cm$^2$