Answer: \(\tfrac{154}{12}\approx12.83\) cm²
Area of sector \(=\dfrac{\theta}{360}\times\pi r^2\); length of arc \(=\dfrac{\theta}{360}\times2\pi r\).
Area of circle \(=\tfrac{22}{7}\times49=154\) cm².
Area of sector \(=\dfrac{30}{360}\times154\) = \(\tfrac{154}{12}\approx12.83\) cm².