Math question, help please!

Q) The diagram below shows a 6-sided shape.
All the measurements are in in centimetres.
The are of this shape is 102cm squared.
Work out the length of the longest side of the shape. (6 marks)

p.s - That's a 4, not a 9.
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I often see these types of question and usually skip them because they're a the back and I have no idea how to start them. Is there a method for this? If so can anyone please tell me. ^^

The method would be to split the shape up into rectangles, of which the lengths are known, and then create an equation for the total area of the shape, which would be equal to the sum of each individual rectangle's area. This equation could then be solved (for x) and the value found used to discover the length of the longest side.

For instance, you could split this shape into one rectangle of height (x + 4) and width (2x), and another of width (4x - 3) and height equal to the total height of the shape (2x + 5) minus the height 'taken' by the first rectangle (x + 4). I'm assuming you know how to work out the area of a rectangle, so this gives you one quadratic equation for the area of the first rectangle and another for the second. The total area of the shape is equal to the area of the first rectangle plus that of the second, hence giving you a quadratic equation for the total area of the rectangle by adding the two quadratic equations together. As the total area of the rectangle is given to you, this leaves you with a quadratic equation to solve (for x). Once you have found x, simply input this value into each of the equations for the lengths of the shape as a whole and the largest value will be your answer (the length of the longest side).