1. **State the problem:** We need to find the area of a trapezium with top base $16$ cm, bottom base $8$ cm, and height $7$ cm. 2. **Formula for the area of a trapezium:** $$\text{Area} = \frac{(a + b)}{2} \times h$$ where $a$ and $b$ are the lengths of the two parallel sides (bases), and $h$ is the height. 3. **Substitute the given values:** $$a = 16, \quad b = 8, \quad h = 7$$ 4. **Calculate the sum of the bases:** $$16 + 8 = 24$$ 5. **Divide by 2:** $$\frac{24}{2} = 12$$ 6. **Multiply by the height:** $$12 \times 7 = 84$$ 7. **Final answer:** The area of the trapezium is $84$ square centimeters.