The area of a sector of a circle of radius 5 cm, formed by an arc of length 3.5 cm, is

### Concept & Formula The area of a sector of a circle can be calculated directly if the arc length $l$ and the radius $r$ are known, bypassing the need to find the central angle. $$Area = \frac{1}{2} \times l \times r$$ ### Step-by-Step Solution * Given radius, $r = 5 \text{ cm}$. * Given arc length, $l = 3.5 \text{ cm}$. * Using the formula: Area $= \frac{1}{2} \times 3.5 \times 5$ Area $= \frac{17.5}{2}$ Area $= 8.75 \text{ cm}^2$ ### Exam Strategy & Shortcut This is a direct formula application. Recognize that $3.5 \times 5 = 17.5$, and half of $17.5$ is $8.75$. You can mentally divide $17$ by $2$ to get $8.5$, and $0.5$ by $2$ to get $0.25$, summing to $8.75$. ### Common Pitfall Students often try to find the angle $\theta$ first using $l = \frac{\theta}{360} \times 2\pi r$, and then plug $\theta$ into the sector area formula. This introduces unnecessary $\pi$ terms and calculation steps, increasing the chance of errors. ### Final Answer Therefore, the correct answer is **8.75 cm²**.