It can be observed from the figure that the lighthouse spreads light across a sector of 80° in a circle of 16.5 km radius.
Area of sector OACB = \(\frac{80°}{360°} \times \pi r ^2\)
= \(\frac{2}{9} \times 3.14 \times 16.5 \times 16.5\)
= \(189.97\,km^2\)