1. **State the problem:** Calculate the total area of the compound figure composed of a red triangle, a blue rectangle, two yellow right triangles, and a small trapezoid as described. 2. **General formula for compound figure area:** $$\text{Total Area} = \text{Area of red triangle} + \text{Area of blue rectangle} + 2 \times \text{Area of yellow triangles} + \text{Area of trapezoid}$$ 3. **Specific formulas for each polygon:** - Triangle area: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ - Rectangle area: $$A = \text{width} \times \text{height}$$ - Trapezoid area: $$A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$$ 4. **Substitute numerical values:** - Red triangle: $$A = \frac{1}{2} \times 4 \times 5 = 10$$ - Blue rectangle: $$A = 4 \times 6 = 24$$ - Yellow triangles (each): $$A = \frac{1}{2} \times 3 \times 2 = 3$$ - Two yellow triangles total: $$2 \times 3 = 6$$ - Trapezoid: $$A = \frac{1}{2} \times (1 + 2) \times 1 = \frac{1}{2} \times 3 \times 1 = 1.5$$ 5. **Calculate total area:** $$\text{Total Area} = 10 + 24 + 6 + 1.5 = 41.5$$ **Final answer:** The total area of the compound figure is **41.5 square centimeters**.