1. **State the problem:** We need to find the area of a trapezium with parallel sides of lengths 5 cm and 30 cm, and a height of 12 cm. 2. **Formula for the area of a trapezium:** $$\text{Area} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$$ 3. **Identify the values:** - Parallel sides: $5$ cm and $30$ cm - Height: $12$ cm 4. **Substitute the values into the formula:** $$\text{Area} = \frac{1}{2} \times (5 + 30) \times 12$$ 5. **Calculate the sum of the parallel sides:** $$5 + 30 = 35$$ 6. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 35 \times 12 = \frac{1}{2} \times 420 = 210$$ 7. **Final answer:** The area of the trapezium is $210$ square centimeters.