# Area of a Rhombus

How to find the area of a rhombus: formula, proof, examples, and their solutions.

## Formula

*A* = (1/2)⋅*ab**A*: area of a rhombus*a*, *b*: diagonals

## Proof

The diagonals of a rhombus

perpendicularly bisect each other.

Then the gray right triangle's legs are

(1/2)*a* and (1/2)*b*.

So the area of the gray right triangle is (1/8)*ab*.

There are 4 right triangles in the rhombus.

So the area of the rhombus is

4 × (1/8)*ab* = (1/2)*ab*.

## Example 1

*a* = 7, *b* = 12*A* = (1/2)⋅7⋅12

## Example 2

See the darker gray right triangle.

Its hypotenuse is 5.

And its leg is 4.

So it's a (3, 4, 5) triangle.

So the green leg is 3.

The diagonals perpendicularly bisect each other.

So the blue segments are 4.

And the green segments are 3.

So *a* = 8, *b* = 6.

*a* = 8, *b* = 6*A* = (1/2)⋅8⋅6