1. **State the problem:** Calculate the area of a composite shape made of a rectangle and a right triangle on top. 2. **Identify dimensions:** Rectangle width = 6 cm, height = 10 cm; Triangle base = 6 cm, height = 5 cm. 3. **Formula for area:** - Rectangle area = base \times height - Triangle area = \frac{1}{2} \times base \times height 4. **Calculate rectangle area:** $$\text{Area}_{rectangle} = 6 \times 10 = 60$$ 5. **Calculate triangle area:** $$\text{Area}_{triangle} = \frac{1}{2} \times 6 \times 5 = \frac{1}{2} \times 30 = 15$$ 6. **Add areas for total area:** $$\text{Total area} = 60 + 15 = 75$$ 7. **Final answer:** The area of the shape is $75$ square centimeters.