Standard +0.3 This is a standard sector/segment problem requiring recall of arc length and sector area formulas (s=rθ, A=½r²θ) to find r and θ, then calculating triangle area to subtract from sector area. The algebra is straightforward (6=rθ and 24=½r²θ gives r=8, θ=0.75) and the method is a common textbook exercise, making it slightly easier than average.
\includegraphics{figure_3}
The diagram shows a sector \(AOB\) of a circle with centre \(O\). The length of the arc \(AB\) is \(6\) cm and the area of the sector \(AOB\) is \(24\) cm\(^2\). Find the area of the shaded segment enclosed by the arc \(AB\) and the chord \(AB\), giving your answer correct to \(3\) significant figures. [6]
\includegraphics{figure_3}
The diagram shows a sector $AOB$ of a circle with centre $O$. The length of the arc $AB$ is $6$ cm and the area of the sector $AOB$ is $24$ cm$^2$. Find the area of the shaded segment enclosed by the arc $AB$ and the chord $AB$, giving your answer correct to $3$ significant figures. [6]
\hfill \mbox{\textit{SPS SPS SM 2025 Q3 [6]}}