 # Rhombus: A very Important Member of the Quadrilateral Family

A rhombus is a special type of parallelogram with four equal sides that makes it completely different. It has a diamond shape and is defined due to the various unique properties that make it different from various other types of quadrilaterals. It is considered to be a very important member of the quadrilateral family as it possesses almost similar properties like that of square and parallelogram but has its own properties that make it a different type of quadrilateral.

## 1. Properties of a Rhombus:

One can easily identify a rhombus through its following properties:

1. Rhombus has four equal sides.

2. The opposite sides of the quadrilateral are parallel to each other.

3. Adjacent angles are supplementary which means the sum of two adjacent angles is 180°.

4. Opposite angles are equal to each other or in other words congruent to each other.

5. Diagonals of a rhombus bisect each other at 90° angles.

6. Two diagonals of a rhombus divide it into four equilateral triangles.

7. Sum of the interior angles of a rhombus is 360°

These properties make the rhombus a unique type of quadrilateral. It is also known as an equilateral quadrilateral due to its unique property of equal sides. Moreover, one can say a rhombus has similar properties to that of a parallelogram and square. However, every rhombus can be termed as a parallelogram but it is not mandatory for a parallelogram to be a rhombus. On the other hand, a rhombus may not be a square but all the squares are rhombuses.

## 2. Shape of a Rhombus:

A rhombus is a special type of quadrilateral that looks similar to a diamond or a kite. It is also referred to as a rhomb, diamond, or lozenge. As all of its sides are equal and parallel to each other it looks somewhat similar to a square and a parallelogram. But due to its unique features and properties, it is considered to be a completely different type of shape and quadrilateral.

It is considered to be a closed shape figure where its four sides are equal to each other and adjacent sides do not make a 90° angle.

## 3. Calculating Area and Perimeter of a Rhombus:

The area of a rhombus is defined as the space enclosed by its four sides. The area of a Rhombus is calculated in cm or meter per square depending upon the measure of the lens of its sides and diagonals.

The area of a rhombus can be calculated by multiplying the measure of its diagonals and diving the resultant value with 2.

Area of rhombus formula – d1 x d2 / 2

Here d1 and d2 are the measures of diagonals of a rhombus.

## There are Two Other Ways of Calculating the Area of a Rhombus

1. Area of a rhombus can be easily calculated by multiplying the measure of its base with its perpendicular height. Since all the sides of a rhombus are equal, any side can be taken as a base. However, the height should be the perpendicular distance between two opposite sides.

Area of a rhombus = base x height

2. Another way of calculating the area of a rhombus is through the use of trigonometry.

Area of Rhombus = (side) ^2 x sin (a)

Where “a” is the value of an angle between two adjacent sides of a rhombus.

The perimeter of a rhombus is the sum of its four sides. Like a Square since all the sites of the rhombus are equal in length, its perimeter formula is also the same. Therefore the perimeter of a rhombus = 4 x side.

Learning about different types of quadrilaterals like rhombus is an essential aspect of geometry. Cuemath is a dedicated company that makes available online resources and information to make the learning process completely convenient. Students are provided with resources so that learning about different quadrilaterals and geometry, in particular, becomes hassle-free. Worksheets, online guidance, and other dedicated support services are made available to make maths fun and easy to grasp.

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