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 $ABCD$, then,

$\overline{AB} \cong \overline{BC} \cong \overline{CD} \cong \overline{DA}$.

and

$\overline{AC} \perp \overline{BD}$. » Read more