A complete answer can be found here however in summary:

• [S] rotate the polygon to match one of its edges with X axis
• compute minmax of X and Y for vertices
• this gives you a candidate for minimum area rectangle (MAR) or MBR
• store the area of (x2-x1)*(y2-y1)
• repeat from [S] for all edges
• find the minimum area which corresponds to MBR
• rotate found [[x1,y1],[x2,y2]] by -angle applied in [S]

Done.

A complete answer can be found here however in summary:

• [S] rotate the polygon to match one of its edges with X axis
• compute minmax of X and Y for vertices
• this gives you a candidate for minimum area rectangle (MAR) or MBR
• store the area of (x2-x1)*(y2-y1)
• repeat from [S] for all edges
• find the minimum area which corresponds to MBR
• rotate found [[x1,y1],[x2,y2]] by -angle applied in [S]

Done.