The figure shows two sectors in which \(AB\), \(CD\) are arcs of concentric circles, centre \(O\) and radii \(\quantity{2k}{cm}\) and \(\quantity{3k}{cm}\) respectively. \(A\hat{O}B\) is \(\frac{3}{4}\) radian and the area \(ABDC\) is \(\quantity{30}{cm^2}\). Find

- the value of \(k\),

What are the areas of the two sectors in terms of \(k\)? Is there a formula we could use?

Is there a similar formula to help with finding arc lengths?