Congruence and Similarity - Map Scales

A designer creates a logo made of three overlapping rectangles, \(A\), \(B\) and \(C\). The ratio of the areas \(A:B:C\) is \(5:10:6\). It is known that \(\frac{1}{5}\) of \(A\) overlaps \(B\) and \(\frac{1}{8}\) of \(B\) overlaps \(C\).

1. Find the ratio of the area of the overlapping (shaded) region to the total area of the logo.
2. If the logo is printed at a scale of \(1:200\), find the actual area in m\(^2\) of the shaded region if the logo area on paper is \(28\) \(\mathrm{cm}^2\).
3. Hence, find the total printing cost if the unit printing cost for the shaded region is \(\$225\) per \(\mathrm{m}^2\) and that for the non-shaded region is \(\$150\) per \(\mathrm{m}^2\).

In all parts, the overlapping region means both intersections \(A\cap B\) and \(B\cap C\) together. The right-hand overlap is only faintly shaded in the supplied diagram.