3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9f5761f9-15d0-499a-992a-c98539f2785c-10_508_874_244_609}
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\caption{Figure 1}
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Diagram not to scale
Figure 1 shows the design for a table top in the shape of a rectangle \(A B C D\). The length of the table, \(A B\), is 1.2 m . The area inside the closed curve is made of glass and the surrounding area, shown shaded in Figure 1, is made of wood.
The perimeter of the glass is modelled by the curve with polar equation
$$r = 0.4 + a \cos 2 \theta \quad 0 \leqslant \theta < 2 \pi$$
where \(a\) is a constant.
- Show that \(a = 0.2\)
Hence, given that \(A D = 60 \mathrm {~cm}\),
- find the area of the wooden part of the table top, giving your answer in \(\mathrm { m } ^ { 2 }\) to 3 significant figures.