Is the area of a parallelogram equal to the magnitude of the length of the diagonal?

Question

I understand that the area of a parallelogram is equal it the cross product of the two vectors that join to form it's two sides. But how about the diagonal of the parallelogram , is the cross product the same as the diagonal's magnitude? Only reason I ask I am having trouble understanding torque. The torque is said to be cross product but I can't see how applying force in the plane of a cross product can result in a force that is perpendicular. Sorry for two part question but the first question really is a bit confusing unless one understands why I am asking it to being with and no matter which question I ask first they must eventually be put together to make sense.