Why the Area of a Rhombus is Half the Product of its Diagonals
A rhombus is a parallelogram with four congruent sides. Since it is a parallelogram, it has also all the properties of a parallelogram. One of these properties is that the diagonals bisect each other. That is, they divide each other into two equal parts.
Another property of a rhombus is that the diagonals are perpendicular. So, summarizing all the properties above, if we have rhombus 
and
.