1. **State the problem:** We have a trapezoid with height $h = 11$ cm, area $A = 550$ cm², and one base $b_1 = 10$ cm. We need to find the length of the other base $b_2$. 2. **Formula for the area of a trapezoid:** $$A = \frac{h(b_1 + b_2)}{2}$$ This formula states that the area is half the height times the sum of the two bases. 3. **Substitute known values:** $$550 = \frac{11(10 + b_2)}{2}$$ 4. **Multiply both sides by 2 to eliminate the denominator:** $$2 \times 550 = 11(10 + b_2)$$ $$1100 = 11(10 + b_2)$$ 5. **Divide both sides by 11 to isolate the sum of bases:** $$\frac{1100}{\cancel{11}} = \cancel{11}(10 + b_2)$$ $$100 = 10 + b_2$$ 6. **Solve for $b_2$:** $$b_2 = 100 - 10 = 90$$ 7. **Final answer:** The length of the other base is $\boxed{90}$ cm.