6.
\includegraphics[max width=\textwidth, alt={}]{fe47eac1-645a-46c6-a2b9-c4ad0bcaa538-2_337_896_694_452}
The diagram shows triangle \(A B C\) in which \(A C = 8 \mathrm {~cm}\) and \(\angle B A C = \angle B C A = 30 ^ { \circ }\).
- Find the area of triangle \(A B C\) in the form \(k \sqrt { 3 }\).
The point \(M\) is the mid-point of \(A C\) and the points \(N\) and \(O\) lie on \(A B\) and \(B C\) such that \(M N\) and \(M O\) are arcs of circles with centres \(A\) and \(C\) respectively.
- Show that the area of the shaded region \(B N M O\) is \(\frac { 8 } { 3 } ( 2 \sqrt { 3 } - \pi ) \mathrm { cm } ^ { 2 }\).