Okay, long time never did this kind of thing but it's actually
quite easy.
From diagram, you know PQ = QC and BP = (1/2)QC
So let BP be 1 unit --> QC = 2 units = PQ
---> 5 units = 30 cm ---> 1 unit = 6 cm
Hence,
PC = PQ + QC = 24 cm
BQ = BP + PQ = 18 cm
Therefore,
Area ABQ = 1/2 * 16 * 18 = 144 cm^2
Area CDP = 1/2 * 16 * 24 = 192 cm^2
---> Area of shaded portion = 144 + 192 - 42 = 294 cm^2 which is
your answer.
And as for the discrepancy in answer, actually if you draw out the
rectangle, you realise that the area of the shaded portion isn't
really 42 cm^2.
That is, the entire diagram has inconsistent dimensions. Your
method is correct and the 294 is also "correct" but because the
dimensions are inconsistent, you'll get different answers.
