Three rectangles and a?

Geometry Level 4

A square, with an area of 324, is divided to four polygons, three of them is a rectangle, the fourth is a hexagon.

The blue rectangle's perimeter is 50, the red's rectangle's area is 63. If the sides of each polygon are integers, then find the maximum possible value of the yellow hexagon's perimeter.

Note : The figure is not drawn to scale.


The answer is 44.

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