1. **Calculate the area of the triangle** The problem: Find the area of a triangle with base 12 cm and height 8 cm. Formula used: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ Calculation: $$\text{Area} = \frac{1}{2} \times 12 \times 8 = \frac{1}{2} \times 96 = 48 \text{ cm}^2$$ 2. **Calculate the area of the circle** The problem: Find the area of a circle with diameter 8 cm. Formula used: $$\text{Area} = \pi \times r^2$$ where radius $r = \frac{\text{diameter}}{2} = \frac{8}{2} = 4$ cm. Calculation: $$\text{Area} = \pi \times 4^2 = \pi \times 16 = 16\pi \text{ cm}^2$$ 3. **Calculate the area of the parallelogram** The problem: Find the area of a parallelogram with base 12 cm and height 6 cm. Formula used: $$\text{Area} = \text{base} \times \text{height}$$ Calculation: $$\text{Area} = 12 \times 6 = 72 \text{ cm}^2$$ 4. **Calculate the area of the trapezoid** The problem: Find the area of a trapezoid with top base 12 cm, bottom base 15 cm, and height 6 cm. Formula used: $$\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$$ Calculation: $$\text{Area} = \frac{1}{2} \times (12 + 15) \times 6 = \frac{1}{2} \times 27 \times 6 = \frac{1}{2} \times 162 = 81 \text{ cm}^2$$ **Final answers:** - Triangle area = 48 cm$^2$ - Circle area = $16\pi$ cm$^2$ - Parallelogram area = 72 cm$^2$ - Trapezoid area = 81 cm$^2$