1. **Problem statement:** A man walks 10 m north and then 20 m east. We need to find his displacement. 2. **Formula:** Displacement is the straight-line distance from the starting point to the final position. Since the man moves north and east, his path forms a right-angled triangle. 3. **Use the Pythagorean theorem:** $$\text{Displacement} = \sqrt{(\text{north distance})^2 + (\text{east distance})^2}$$ 4. **Substitute values:** $$= \sqrt{10^2 + 20^2} = \sqrt{100 + 400} = \sqrt{500}$$ 5. **Simplify:** $$= \sqrt{100 \times 5} = 10\sqrt{5} \approx 22.36$$ meters 6. **Explanation:** The displacement is the shortest distance from the start to the end point, which is the hypotenuse of the right triangle formed by the north and east movements. **Final answer:** The displacement is approximately $22.36$ meters.