Properties of Rhombi

A rhombus is a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides. Here is a diagram of a rhombus.

Perimeter and Area

The perimeter of a rhombus is $4s$, where $s$ is a side length. The area of a rhombus is $\frac{pq}{2}$, where $p$ and $q$ are lengths of diagonals. The perimeter is easy to get -- just add up all the sides. The area, however, is a different matter.

How to Get the Area of a Rhombus

This is a rhombus:

Notice the area of the rhombus is just the four right triangles that it consists of. These right triangles have sides $\frac p2$ and $\frac q2$. Using the area formula and multiplying by 4, we have: $$A= 4((pq/4)/2)=4(pq/8)=pq/2.$$

Therefore, the area of a rhombus is $\frac{pq}{2}$, where $p$ and $q$ are diagonal lengths.

Symmetry

A rhombus has two lines of symmetry. Here they are.

Here's a little quiz about rhombuses:

Solution to the last question

Rhombi are pretty cool, don't you think?

~ Abigale Kim, a+bi