1. **State the problem:** We need to find the height of a trapezium given its area and the lengths of the two parallel sides. 2. **Formula:** The area $A$ of a trapezium is given by $$A = \frac{(a + b)}{2} \times h$$ where $a$ and $b$ are the lengths of the parallel sides, and $h$ is the height. 3. **Given values:** - $a = 4$ cm - $b = 6$ cm - $A = 15$ cm$^2$ 4. **Substitute the known values into the formula:** $$15 = \frac{(4 + 6)}{2} \times h$$ 5. **Simplify the expression:** $$15 = \frac{10}{2} \times h$$ $$15 = 5h$$ 6. **Solve for $h$:** $$h = \frac{15}{5} = 3$$ 7. **Answer:** The height of the trapezium is $3$ cm.