First, I would fix a thin needle on a stand. Then, I would penetrate the triangle with a thin needle so that the triangle lies in a vertical plane. If the triangle keeps its position no matter how I rotate it, I hit the center of gravity and all what is left is to mark it and measure the distance to the closest side.
If it rotates due to gravity, I need to change the point where the needle penetrates the triangle until I find the center of gravity.
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