Area of a Rhombus Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the area of a rhombus?

Answer

Area of a rhombus
A = ½ · d · e

Here d is the first diagonal, e is the second diagonal. The result comes out in square units.

Where the formula comes from

A = ½ · d · e

The diagonals of a rhombus cross at right angles and cut each other in half, so they slice it into four right triangles. Put together, those four fill exactly half of the rectangle d by e drawn around the rhombus.

Worked examples

Let d = 10, e = 6. Then the area of a rhombus = 30 square units.

Let d = 7.4, e = 5. Then the area of a rhombus = 18.5 square units.

The common mistake

Squaring the side, as for a square. A rhombus has four equal sides, but unless it IS a square its angles are not right, and then a² overstates the area — the same trap as with a parallelogram, which a rhombus is. A square is the one rhombus where a² happens to be exact.

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the area of a rhombus? (The answer is: A = ½ · d · e). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula (e = 6)

If d =Area
13 square units
26 square units
39 square units
412 square units
515 square units
1030 square units

FAQ

What is the formula for the area of a rhombus?

Area of a rhombus A = ½ · d · e

Where does this formula come from?

The diagonals of a rhombus cross at right angles and cut each other in half, so they slice it into four right triangles. Put together, those four fill exactly half of the rectangle d by e drawn around the rhombus.

What is the most common mistake here?

Squaring the side, as for a square. A rhombus has four equal sides, but unless it IS a square its angles are not right, and then a² overstates the area — the same trap as with a parallelogram, which a rhombus is. A square is the one rhombus where a² happens to be exact.

How do I use this formula?

Put your own numbers in place of the letters. With d = 7.4, e = 5, for instance, the formula A = ½ · d · e gives = 18.5 square units.