Discussion
The area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is?
Answer: C
A sector is a triangle-like wedge whose "base" is its arc and whose "height" is the radius:
\[ A = \frac{1}{2} \times r \times \text{arc length} \]
\[ = \frac{1}{2} \times 5 \times 3.5 = 8.75 \text{ cm}^{2} \]
This form needs no angle at all. It follows from \( A = \tfrac{\theta}{2\pi}\pi r^{2} \) and \( \text{arc} = r\theta \), which combine to give exactly \( \tfrac{1}{2}r \times \text{arc} \).
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