
Area of a rhombus
Three different ways to calculate the area of a
rhombus are given below, with a formula for each.
Try this Drag the orange dots on each vertex
to reshape the rhombus. The area will be continuously calculated using the "base times height" method.
A rhombus
is actually just a special type of parallelogram.
Many of the area calculations can be applied to them also. Choose a formula based on the values you know to begin with.
1. The "base times height" method
First pick one side to be the base. Any one will do, they are all the same length.
Then determine the altitude  the perpendicular distance from the chosen base to the opposite side.
The area is the product of these two, or, as a formula:

where
b is the length of the base
a is the altitude (height).


Use the calculator on the right to calculate the area of the trapezoid given base (side) length and
altitude (perpendicular height).
Enter any two values and the missing one will be calculated.
For example, enter the area and base length, and the height needed to get that area is calculated.

2. The "diagonals" method
Another simple formula for the area of a rhombus when you know the lengths of the diagonals.
The area is half the product of the diagonals. As a formula:

where
d_{1} is the length of a diagonal
d_{2} is the length of the other diagonal


3. Using trigonometry
If you are familiar with trigonometry, there is a handy formula when you know the length of a side and any angle:

where
s is the length of any side
a is any interior angle
sin is the sine function
(see Trigonometry Overview)


It may seem odd at first that you can use any angle since they are not all equal. But the angles are either equal or
supplementary,
and supplementary angles have the same sine.
Related polygon topics
General
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
Named polygons
(C) 2009 Copyright Math Open Reference. All rights reserved

COMMON CORE
Math Open Reference now has a Common Core alignment.
See which resources are available on this site for each element of the Common Core standards.
Check it out
