Decompose the rectangle along the diagonal and recompose the two pieces to make a different shape. How does the area of this new shape compare to the area of the original rectangle? Explain how you know

Its the same area as the original shape.

Step-by-step

If you descompose a original area into smaller pieces. The mathematical process of cutting areas won't add or substract area. Even of you cut the original area to infinitesimal size pieces, the infinite number of pieces will sum up the same area as original area.