Of the two square fields, the area of one is 1 hectare while the other one is broader by 1%. The difference in their areas is

### Concept & Unit Conversion and Percentage Increase This problem combines metric area conversions with percentage changes in linear dimensions. $$ 1 \text{ hectare (ha)} = 10,000 \text{ m}^2 $$ ### Step-by-Step Solution * **Step 1:** The area of the first square field is $1 \text{ hectare}$, which equals $10,000 \text{ m}^2$. * **Step 2:** Find the side length of the first field. Side $s_1 = \sqrt{10000} = 100 \text{ m}$. * **Step 3:** The second field is "broader by 1%". This means its side length is 1% larger. * **Step 4:** Calculate the new side length: $s_2 = 100 + (1\% \text{ of } 100) = 100 + 1 = 101 \text{ m}$. * **Step 5:** Calculate the area of the second field: $A_2 = 101^2 = 101 \times 101 = 10,201 \text{ m}^2$. * **Step 6:** Find the difference in their areas: $10,201 \text{ m}^2 - 10,000 \text{ m}^2 = 201 \text{ m}^2$. ### Exam Strategy & Shortcut Use the successive percentage formula $x + y + \frac{xy}{100}$ for area changes when sides change by a percentage. With a 1% increase in side, the area increases by $1 + 1 + \frac{1 \times 1}{100} = 2.01\%$. $2.01\%$ of $10,000 \text{ m}^2$ is $201 \text{ m}^2$. This skips calculating the new side length and squaring it entirely. ### Common Pitfall A frequent mistake is calculating 1% of the *area* directly instead of the side, resulting in an incorrect difference of $100 \text{ m}^2$. ### Final Answer Therefore, the correct answer is **201 m$^2$**.