I would divide it into 2 triangles and get the centeroid of each (middle of one side, 1/3 towards opposite corner). Then take a line between the two centroids, apply a mass at each end, and you have a simple equation of finding the center of gravity of that line.
I'm an engineer, not a mathematician, so the above would be my starting point and then validate the method perhaps by dividing the area into different triangles.
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