3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{dfb4b2bc-4bc8-4e5b-9b13-ffe4fbde1b4f-08_885_1388_260_287}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the design for a badge.
The design consists of two congruent triangles, \(A O C\) and \(B O C\), joined to a sector \(A O B\) of a circle centre \(O\).
- Angle \(A O B = \alpha\)
- \(A O = O B = 3 \mathrm {~cm}\)
- \(O C = 5 \mathrm {~cm}\)
Given that the area of sector \(A O B\) is \(7.2 \mathrm {~cm} ^ { 2 }\)
- show that \(\alpha = 1.6\) radians.
- Hence find
- the area of the badge, giving your answer in \(\mathrm { cm } ^ { 2 }\) to 2 significant figures,
- the perimeter of the badge, giving your answer in cm to one decimal place.
| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |