OpenCV - Find skewed rectangle

I want to draw a "bounding box" around a skewed rectangle. I thought I could use the cvMinAreaRect2() function but it only handles the rotation, see this image:

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Is there any function to solve this? If not, any ideas how to implement it?

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Compute both MinAreaRect and ConvexHull. Then, for each of the four points found by MinAreaRect, find the corresponding nearest point in the convex hull.