1. **State the problem:** Calculate the total area of a compound figure shaped like a spaceship composed of a red triangle, a blue rectangle, two yellow right triangles, and a blue trapezoid with given dimensions. 2. **General formula for compound figures:** The total area is the sum of the areas of all individual polygons: $$\text{Total Area} = \sum \text{Area of each polygon}$$ 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: base = 4 cm, height = 5 cm $$A_\text{red triangle} = \frac{1}{2} \times 4 \times 5 = 10$$ - Blue rectangle: width = 4 cm, height = 6 cm $$A_\text{rectangle} = 4 \times 6 = 24$$ - Yellow right triangles (2 identical): base = 2 cm, height = 3 cm each $$A_\text{yellow triangle} = \frac{1}{2} \times 2 \times 3 = 3$$ Total for two yellow triangles: $$2 \times 3 = 6$$ - Blue trapezoid: top base = 2 cm, bottom base = 2.5 cm, height = 1 cm $$A_\text{trapezoid} = \frac{1}{2} \times (2 + 2.5) \times 1 = \frac{1}{2} \times 4.5 = 2.25$$ 5. **Calculate total area:** $$\text{Total Area} = 10 + 24 + 6 + 2.25 = 42.25$$ **Final answer:** The total area of the compound spaceship figure is **42.25 cm\textsuperscript{2}**.