1. The problem is to find the missing base of a trapezium given the area, one base, and the height. 2. The formula for the area of a trapezium is: $$\text{Area} = \frac{(\text{base}_1 + \text{base}_2)}{2} \times \text{height}$$ 3. We know the area $8.8$, one base $4.2$, and the height $6$. We need to find the other base $b$. 4. Substitute the known values into the formula: $$8.8 = \frac{(4.2 + b)}{2} \times 6$$ 5. Simplify the right side: $$8.8 = 3 \times (4.2 + b)$$ 6. Divide both sides by 3 to isolate the sum of the bases: $$\frac{8.8}{3} = 4.2 + b$$ $$\cancel{3} \frac{8.8}{\cancel{3}} = 4.2 + b$$ 7. Calculate $\frac{8.8}{3}$: $$2.9333 = 4.2 + b$$ 8. Subtract $4.2$ from both sides to solve for $b$: $$2.9333 - 4.2 = b$$ $$\cancel{4.2} 2.9333 - \cancel{4.2} = b$$ 9. Calculate the result: $$b = -1.2667$$ 10. The other base is approximately $-1.27$ cm, which is not possible for a trapezium base length. This suggests an inconsistency in the given values or a misunderstanding of the problem. Final answer: The calculated other base length is approximately $-1.27$ cm, which is not physically valid given the inputs.