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# Rhombus Area Calculator

Rhombus and its propertiesRhombus area formulaRhombus perimeterHow to find the area of a rhombus?Is square a rhombus? Or is a rhombus a parallelogram?FAQs

The rhombus area calculator is an excellent tool to determine the area of a rhombus, as well as its perimeter and other characteristics: diagonals, angles, side length, and height.

Have a look at many ways you can find the diamond area: given diagonals of a rhombus, using base and height, side, and any chosen angle... Are you still wondering how to find the area of a rhombus or rhombus perimeter? Check the rhombus area formulas below, or just experiment with the tool.

## Rhombus and its properties

A rhombus is a simple quadrilateral with all sides equal (see quadrilateral calculator). The other names are an equilateral quadrilateral or a diamond (like the one from playing cards ♢).

The fundamental properties of a rhombus are:

• The two diagonals of a rhombus are perpendicular and bisect each other;
• Its diagonals bisect opposite angles; and
• Opposite angles have equal measure.

Every rhombus is a parallelogram and a kite. So might also be interested in our parallelogram area calculator and the kite area calculator.

## Rhombus area formula

There are three useful formulas for the calculation of the area of the rhombus:

1. Knowing base and height:

area = base × height

2. Knowing the diagonals of a rhombus:

area = (e × f)/2

3. Knowing the side s and any (!) angle:

area = s² × sin(angle)

Why can we use any angle in the last rhombus area formula? Because we know that two adjacent angles are supplementary, and sin(angle) = sin(180° - angle).

There are other variations of those equations (e.g., calculating the area given height and angle), but they are only simple trigonometric transformations of those three most popular rhombus area formulas.

## Rhombus perimeter

Finding the rhombus perimeter is trivial if we know the side length – it's 4 × a. But what if we know only the diagonals of a rhombus? Let's check:

1. We know that diagonals are perpendicular and bisect each other. So the rhombus is nothing else than four congruent triangles, with legs equal to e/2 and f/2.

2. All we need to do is find the hypotenuse of the triangle. You can use here the right triangle calculator or Pythagorean theorem calculator.

3. Multiply by 4 the obtained hypotenuse value. It's your rhombus perimeter!

Also, you can use this formula:

• perimeter = 4 × √(e/2)² - (f/2)²)

Or just type the lengths of the diagonals into the rhombus area calculator!

## How to find the area of a rhombus?

Are you still pretty unsure how to use the calculator? Let's show its potential with a simple example:

1. Type the first given value you have. Let's assume its side = 10 in.

2. Type the second given value. For example, an angle equal to 30°.

3. Wow! The rhombus area calculator displays all the other values – area, height, perimeter, angle, and diagonals. Impressive, isn't it?

Our tool is really flexible – if it's possible to calculate, it will do it. Usually, two given values are enough. Give it a try!

## Is square a rhombus? Or is a rhombus a parallelogram?

The answer is yes to both questions. Every square is a rhombus, as for a rhombus, the only necessary condition is that it needs to have all sides of equal length. As you know perfectly well, a square needs to have all sides equal and all four equal angles so it fulfills the conditions to be a rhombus.

Similarly, a rhombus is a parallelogram, as any shape needs to have two pairs of parallel sides to be a parallelogram – and the rhombus has them. So the rhombus is always a parallelogram, but a parallelogram is a rhombus only in a special case – for a parallelogram with four sides of equal length.

FAQs

### How to find the area of a rhombus with its given sides?

To find the area of a rhombus, you need both its side length s and any one angle α:

1. Multiply the side length by itself to obtain its square:

s × s = s²

2. Multiply this with the sine of the angle α to obtain A, the area of the rhombus:

A = s² × sin(α)

3. Verify the result using our rhombus area calculator.

### How do I find the area of a rhombus with its diagonals?

Finding the area of a rhombus from its diagonals e and f is easy:

1. Multiply the diagonal lengths e and f:

e × f

2. Divide the result by 2 to obtain A, the area of the rhombus:

A = (e × f) / 2

3. Verify the result using our rhombus area calculator.

### How do you find the area of a rhombus with one diagonal and perimeter?

Finding the area of a rhombus from its diagonal e and perimeter p is a little tricky:

1. Multiply the perimeter with itself and divide it by 4:

(p × p) / 4 = p² / 4

2. Subtract the square of the diagonal length e from this result:

(p² / 4) - e²

3. Take the square root of this value to obtain the other diagonal f:

f = √[(p²/4) - e²]

4. Multiply the two diagonals and divide the result by 2 to obtain the rhombus's area:

A = (e × f)/2

### What is the area of a rhombus with diagonals of 8 and 10?

The area of a rhombus whose diagonals are 8 and 10 feet is 40 square feet. To find this answer, follow these steps:

1. Multiply the diagonal lengths, which are 8 feet and 10 feet:

8 × 10 = 80 ft²

2. Divide the result by 2 to obtain A, the area of the rhombus:

A = 80/2 = 40 ft²

3. Verify the result using our rhombus area calculator.