First connect BD, cross A and C, and make straight EF box GH parallel to BD. Then make any two parallel lines pass through B and D, and intersect EF and gh at E, F, G and H respectively.

If you don't understand why the area doubles, you can make AM and CN parallel to EH and FG through A and C respectively. The area of triangle AEB = triangle AMB, and so on, it is a parallelogram with double area.