I understand Euclid's way of proving this. But, the book also says that I can prove this by decomposing one parallelogram into pieces, and then forming another parallelogram by combining those pieces together.

I was thinking of dividing one parallelogram into infinitely small rectangles, and then combine them again in the contour of another parallelogram, like Riemann sum.

But I am also assuming that this is not what author wants because calculus is not yet covered in the book. By using basic properties of parallelograms, how can you prove this postulate?