Let A=[abcd].

How could we show that ad−bc is the area of a parallelogram with vertices (0,0), (a,b), (c,d), (a+b,c+d)?

Are the areas of the following parallelograms the same?

(1) parallelogram with vertices (0,0), (a,b), (c,d), (a+c,b+d).

(2) parallelogram with vertices (0,0), (a,c), (b,d), (a+b,c+d).

(3) parallelogram with vertices (0,0), (a,b), (c,d), (a+d,b+c).

(4) parallelogram with vertices (0,0), (a,c), (b,d), (a+d,b+c).

Thank you very much.

**Answer**

Spend a little time with this figure due to Solomon W. Golomb and enlightenment is not far off:

(Appeared in *Mathematics Magazine*, March 1985.)

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