15.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f39ade34-32e2-4b5c-b80a-9663c6a65c87-26_780_871_242_539}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows the design for a logo.
The logo is in the shape of an equilateral triangle \(A B C\) of side length \(2 r \mathrm {~cm}\), where \(r\) is a constant.
The points \(L , M\) and \(N\) are the midpoints of sides \(A C , A B\) and \(B C\) respectively.
The shaded section \(R\), of the logo, is bounded by three curves \(M N , N L\) and \(L M\).
The curve \(M N\) is the arc of a circle centre \(L\), radius \(r \mathrm {~cm}\).
The curve \(N L\) is the arc of a circle centre \(M\), radius \(r \mathrm {~cm}\).
The curve \(L M\) is the arc of a circle centre \(N\), radius \(r \mathrm {~cm}\).
Find, in \(\mathrm { cm } ^ { 2 }\), the area of \(R\). Give your answer in the form \(k r ^ { 2 }\), where \(k\) is an exact constant to be determined.