Answer:
[tex]32\:\mathrm{m^2}[/tex]
Step-by-step explanation:
When cut by a diagonal, the parallelogram will be divided into two congruent triangles. By definition, congruent polygons have equal areas. Therefore, let the area of each of the triangle be [tex]x[/tex]:
[tex]x+x=64,\\2x=64,\\x=\frac{64}{2}=\boxed{32\:\mathrm{m^2}}[/tex]
