A rhombus area calculator is a useful math tool for calculating the area, height, angle, and other rhombus parameters. Since there are many ways to find the area, we listed the formulas below and other important information regarding the area of a rhombus, its uses, and its characteristics.  

Rhombus and its properties

Rhombus, by definition, in Euclidian geometry, is a special parallelogram with opposite sides equal and parallel. The Rhombus can be square and in the shape of a diamond if it has two acute and obtuse angles. Rhombus has many properties, of which the most important are: 

  • All sides of the Rhombus are equal.
  • The opposite sides are parallel.
  • The sum of adjacent angles is equal to 180 degrees.
  • Rhombus doesn’t have a circumscribing circle.
  • If one of the sides of a rhombus is equal to the shorter diagonal, two congruent equilateral triangles are formed.

Area of Rhombus Formula

Depending on the parameters of a Rhombus, you can use different formulas to calculate the area, which are,

Formula using base and height

Area = height*base

Ex: if we have a side length of a Rhombus of 6cm, and the height is 10cm, the formula would be:

A= h^2 * b => A= 10cm^2 * 6cm => A=60cm^2

Formula using diagonals

The area of a Rhombus is equal to the product of the lengths of diagonals divided by half. The formula is given when the diagonals are known, Area=\frac{(d1*d2)}{2}cm^2 (also all other units) in which d1 and d2 are diagonals of the Rhombus. 

Formula when side and angles are known

When calculating the area of the Rhombus this way, we are using trigonometric. Area = side^2 \cdot sin(A)units^2, where “A” is an interior angle.

Rhombus perimeter

A rhombus’ perimeter is equal to the sum of its sides. A rhombus is a quadrilateral with the same length on all four sides. It is calculated by summing the lengths of all sides. As all four sides of a Rhombus are equal, the formula for perimeter is P= 4 \cdot s, where “s “is the side of the Rhombus

How to find the area of a Rhombus?

Let’s make a Rhombus with sides with four angles A, B, C, D. we can connect diagonals d1 and d2 with each having an opposite angle. The height is given by drawing a perpendicular line from one side to the other. 

Our Rhombus has four equal sides AB, BC, CD, DA, and four angles where opposite ones are equal \angle a=\angle c \, and \, \angle b=\angle d. The diagonals d1 and d2 are only equal in length in squares. The height h is the length from one side to the opposing side when the Rhombus lies with two sides horizontal (flat).

If you know the lengths of any side, since they are equal, you know the length of all sides. The same goes with angle. To find the area, you need to know the height of the Rhombus. Our calculator for finding the area of Rhombus has all parameters in it, so it is easy to calculate. 

Is square a Rhombus? Or is a Rhombus a parallelogram?

The answer to both questions is yes. The only condition for a Rhombus is that it needs to have all sides equal, so every square is a Rhombus. Also, a Rhombus is a parallelogram, as it needs to have two pairs of parallel sides for it to be called as such. A parallelogram is a Rhombus only in one case- a parallelogram that has four equal sides, but a Rhombus is always a parallelogram. 

Frequently Asked Questions

Are all squares Rhombuses?

Yes, all squares are rhombuses because a rhombus is a parallelogram that has four equal sides, and a square is that and also has four equal angles. So, according to these definitions, a square is a rhombus; however, not all rhombuses are squares.

Are all rhombuses parallelograms?

All rhombuses are parallelograms, but not all parallelograms are rhombuses because they need to have only opposite sides equal, compared to rhombuses, which need to have all sides in equal lengths.

Are the diagonals of a rhombus congruent?

No, the diagonals of a rhombus in most cases are different in lengths, where one is longer than the other, except in the case of a square, where diagonals are equal.

Are all sides of a rhombus equal?

A rhombus has all of its sides equal, which is the definition of a rhombus.

What are the two formulas for the area of a rhombus?

A= h^2 x b
The first formula uses sides and the height of a rhombus to calculate the area. In contrast, the second is calculated using diagonals.

How can I find the area of a rhombus rectangle?

A rhombus that is a rectangle is a square, and we can calculate the area by applying the formula A=s^2, where s is a side, and side squared is the area of a square.

Can you find the area of a rhombus with only the perimeter?

In most cases, you will need more characteristics of the given Rhombus, such as height or diagonal. Still, in the case of a square, the perimeter is equal to the sum of four sides, P=4\cdot s. So, having that in mind, the only Rhombus that can be calculated with only the perimeter is a square.