1. **Problem Statement:** Find the area of a square given its diagonal length is 11 m. 2. **Formula and Rules:** For a square with side length $s$ and diagonal length $d$, the relationship is given by the Pythagorean theorem: $$d = s\sqrt{2}$$ 3. **Find the side length $s$:** $$s = \frac{d}{\sqrt{2}} = \frac{11}{\sqrt{2}}$$ 4. **Rationalize the denominator:** $$s = \frac{11}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{11\sqrt{2}}{2}$$ 5. **Calculate the area $A$ of the square:** $$A = s^2 = \left(\frac{11\sqrt{2}}{2}\right)^2 = \frac{11^2 \times 2}{2^2} = \frac{121 \times 2}{4} = \frac{242}{4}$$ 6. **Simplify the fraction:** $$A = \frac{\cancel{242}^{121} \times 2}{\cancel{4}^2} = 60.5$$ 7. **Final answer:** The area of the square is $60.5$ square meters.