Rhombus is a four sided geometrical figure with a shape like diamond. It is a parallelogram which has two sets of parallel sides, equal opposite sides and equal opposite angles. It is a quadrilateral with all four sides of equal length. In other words, it falls under the classification equilateral quadrilateral. Diagonals of this quadrilateral cut each other at their halves and bisect each other at vertex angles. Diagonals are congruent while adjacent angles are supplementary to each other. Few examples of rhombus that we can encounter in real time are kites, the diamond cards in the stack of playing cards, etc. Measures of rhombus oblige the general rule of a parallelogram that the sum of squares of all sides is equal to the sum of squares of the diagonals.

How to find area of a Rhombus?

There are several ways to arrive at the area of a rhombus based on what measurements are known.

• When side length and height are given:

When all the dimensions are intact and precisely given, the area of a rhombus is quite easy to find. A straight formula can be applied and area is calculated. In the above picture, the sides of the rhombus are named ‘a’, height as ‘h’ and diagonals‘d’. This is the simplest means of evaluating the area. Product of side length and height constitutes the area.

Area A1 = a * h;

• When side length and any one angle is given:

In some cases where height is unknown and one of the angles is known, area can be calculated by multiplying side length and sine squared of the angle.

Area A1 =a*sin²P or a*sin²Q or a*sin²R or a*sin²S;

• When only measures of diagonals are known:

The half of the product of diagonals gives the area of a rhombus.

Area A1 = (d1*d2)/2;

• When side length and inradius is known:

Inradius is the radius of a circle that is inscribed inside the rhombus. In such cases, twice the product of the side length and inradius gives the area.

Area A1=2*a*r;

• Magnitude of vectors:

Adjacent sides of a rhombus form a vector. So, the area can be calculated by computing the magnitude of the vector product of two vectors.

To use vectors for area calculation of rhombus, you need to first work out the Cartesian coordinates. Meaning, if a rhombus is placed on an X and Y axes, the four sides (P, Q, R and S) as x₁,y₁, x₂,y₂, x₃, y₃ and x₄,y₄. 

Area A1 =x₁y₂-x₂y₁;

Therefore, area of a rhombus can be calculated by using various methods. A rhombus can ideally be split into two triangles because of the bisecting diagonals. This key property helps to evaluate the total area by framing different formulae linearly and trigonometrically.