Rhombus area formula - Math Open Reference

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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.

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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).

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
d₁ is the length of a diagonal
d₂ is the length of the other diagonal

2. 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