Draw the graph of \(y = \sin x\) for \(0 \leq x \leq \pi\), plotting points with \(x\)-coordinates at intervals of \(\dfrac{\pi}{6}\), and labelling them \(O, A, B, C, D, E, F\) successively.

Calculate the area of the polygon \(OABCDEF\) by dividing it into strips parallel to the \(y\)-axis, or otherwise. Hence give an approximation to \[\int_0^{\pi/2}\sin x \:dx.\]