Properties

The rhombus is categorized as a special kind of quadrilateral parallelogram. These qualities each supply the rhombus with their properties.
Since it is a quadrilateral, the following properties apply:

• 4 sides meet to form 4 vertices
• the sum of all 4 angles is 360 degrees

Because it also is a parallelogram, the following properties apply:

• 2 pairs of opposite parallel sides
• 2 pairs of opposite angles are equal to one another
• the sum of consecutive (not opposite, but rather next to each other) angles is 180 degrees.

In addition to these, the rhombus has its own unique properties:

• 4 sides of the same length
• 2 diagonals (segments connecting opposite vertex points) meet to form 4 90degree angles and divide each vertex angle in half

This can be hard to visualize, so proved below is a diagram illustrating these properties.

Now that how the rhombus is formed has been established, what math questions follow? Well the perimeter is pretty straightforward. It's formula is the same as a squares. P=(4)(s) where s is side length.
As for area, there's quite a few different methods depending on the information being given.

• Given side and height, which doesn't often happen, A = (s)(h)
• Given 2 diagonals, A = (d*D)/2
• Given side and angle, A = (s^2)(sin(angle))

Memorizing formulas can be hard and not at all fun. And what if you haven't learned about trig yet? There's another way, thankfully, by reconfiguring the shape. Or dicing it up and rearranging it into a figure with a much simpler formula. Watch the following video or jump right into the applet.


Go ahead and jump into the applet! Test out a practice problem if you'd like.

:)

Up Next: See the Rhombus' Use In 3D Figures
Return to Rhombus Main Page

References:
Area Formula: Rhombus
Area of a Rhombus