1. **State the problem:** Calculate the area of a trapezium with parallel sides of lengths 7 cm and 3 cm, and a height of 6 cm. 2. **Formula for the area of a trapezium:** $$\text{Area} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$$ 3. **Apply the values:** $$\text{Area} = \frac{1}{2} \times (7 + 3) \times 6$$ 4. **Simplify inside the parentheses:** $$\text{Area} = \frac{1}{2} \times 10 \times 6$$ 5. **Multiply:** $$\text{Area} = \frac{1}{2} \times 60$$ 6. **Calculate the final area:** $$\text{Area} = 30$$ 7. **Answer:** The area of the trapezium is 30 square centimeters.