## Derivation of the Area of a Rhombus

A rhombus is a parallelogram whose sides are congruent. The diagonals of rhombus are perpendicular to each other. They also bisect each other. In this post, we are going to find the general formula for finding the area of a rhombus using these properties. We are going to learn two methods.

Method 1

Consider the rhombus below.

We can divide it into two congruent triangles using diagonal $d_1$. Since the diagonals of a rhombus are perpendicular to each other, we can use $d_1$ as base and one half of $d_2$ as the height of the upper triangle (Why?). If we let $A_T$ be the area of the upper triangle, then, calculating its area, we have  » Read more

## 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