Area of a Rhombus

Area of a Rhombus

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

Formula

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

A = (1/2)⋅ab

A: Area of a rhombus
a, b: Diagonals

Example 1

Find the area of the given rhombus. AC = 12, BD = 7.

The diagonals area 12 and 7.

So A = (1/2)⋅12⋅7.

(1/2)⋅12 = 6

6⋅7 = 42

So A = 42.

Example 2

Find the area of the given rhombus. Segment from bisected diagonal: 4, Side: 5.

The diagonals perpendicularly bisect each other.

So the right blue segment is 4.
Then the blue diagonal is, 4 + 4, 8.

And draw a right angle like this.

See this right trianle.

Starting from the shortest side,
the sides are ([brown side], 4, 5).

So this right triangle is a (3, 4, 5) right triangle.

Pythagorean triples

So the brown side is 3.

The brown diagonal is also bisected.

So the upper brown segment is 3.

Then the brown diagonal is, 3 + 3, 6.

For the rhombus,
the diagonals are 8 and 6.

So A = (1/2)⋅8⋅6.

(1/2)⋅8 = 4

4⋅6 = 24

So A = 24.