Problem

In circle $\mathrm{R}$ with $m \angle Q R S=42^{\circ}$ and $Q R=4$, find the area of sector QRS. Round to the nearest hundredth.

Answer

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Answer

\(\boxed{11.42}\) is the area of sector QRS

Steps

Step 1 ：Convert angle from degrees to radians: \(\theta = 42 \times (\frac{\pi}{180}) = 0.733\)

Step 2 ：Find the radius using chord length formula: \(4 = 2 \times r \times \sin(\frac{\theta}{2}) \Rightarrow r \approx 5.58\)

Step 3 ：Calculate the area of sector QRS: \(A = \frac{1}{2} \times r^2 \times \theta \approx 11.42\)

Step 4 ：\(\boxed{11.42}\) is the area of sector QRS

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