The area of a square field is 0.5 hectare. Its diagonal would be

### Concept & Formula The key to solving this problem is knowing the conversion factor between hectares and square meters, and the relationship between a square's area and its diagonal. $$ \text{Area of a square} = \frac{1}{2} \times (\text{Diagonal})^2 $$ ### Step-by-Step Solution * **Step 1:** Convert the given area into square meters. We know that $1 \text{ hectare} = 10,000 \text{ m}^2$. * **Step 2:** Area $= 0.5 \text{ hectare} = 0.5 \times 10,000 \text{ m}^2 = 5,000 \text{ m}^2$. * **Step 3:** Use the area-diagonal formula: $5,000 = \frac{1}{2} \times d^2$. * **Step 4:** Multiply both sides by 2: $d^2 = 10,000$. * **Step 5:** Take the square root: $d = 100 \text{ m}$. ### Exam Strategy & Shortcut Memorize standard land area conversions like hectares to square meters ($1 \text{ ha} = 10^4 \text{ m}^2$). Instead of finding the side length first ($\sqrt{5000}$) and then multiplying by $\sqrt{2}$, directly use the $\text{Area} = \frac{d^2}{2}$ formula to save time. ### Common Pitfall A frequent mistake is not knowing the hectare-to-meter conversion, or incorrectly assuming $1 \text{ hectare} = 100 \text{ m}^2$ or $1,000 \text{ m}^2$, which leads to incorrect orders of magnitude in the final answer. ### Final Answer Therefore, the correct answer is **100 m**.