A rhombus is a flat shape simple quadrilateral having four sides of equal length. Rhombus is also known as diamond (diamond suit in playing cards) or lozenge (rhombus having 45$^{\circ}$). A rhombus is a called as parallelogram if its opposite sides will be parallel and opposite angles will be equal.
Every square is a rhombus but a rhombus need not be a square. Similarly rhombus is a parallelogram but a parallelogram need not be rhombus.

## Properties of Rhombus

Given below are the important properties of rhombus:

1. In a rhombus all sides are congruent and rhombus forms two congruent isosceles triangles.

2. Rhombus is an equilateral parallelogram.

3. In a rhombus any side can be considered as a base altitude.

4. The altitude is the perpendicular distance to two sides and the diagonals of a rhombus( p and q) bisect each other at right angle.

5. In a rhombus diagonals will not be of same length.

6. Adjacent angles of a rhombus are supplementary.

## Area of a Rhombus

Through different methods one can calculate the area of a rhombus. Given below are the three different methods used commonly to find the area of a rhombus.

1. Base times height method

Firstly choose any one side as the base as all the sides will be of same length. Next find the altitude, which will be the perpendicular distance from the chosen base to the opposite side. Area will be the product of base and altitude.

Area = b $\times$ a
where b : Length of the base
a : Altitude

2. Trigonometry method

In a figure if the length of a side and any angle is known then trigonometry method can be used. Because the angles can either be equal or supplementary. The formula is
Area = $S^{2}$ Sin a
where S: length of any side
a : interior angle

3. Diagonals method

If the length of the diagonals is known then area is said to be half the product of the diagonals.

Area = $\frac{D_{1} \ D_{2} }{2}$

$D_{1}$ : Length of the first diagonal.
$D_{2}$ : Length of the second diagonal.

## Perimeter of Rhombus

The perimeter of a rhombus is the total distance around the outside (polygon) found by adding the length of each side. As all the sides are of same length it is four times the length of a side.

Perimeter = 4S
where S : Length of the side

## Rhombus Symmetry

Rhombus is a convex quadrilateral having the sides of same length. A rhombus has two lines of symmetry which are formed by connecting one vertex to the opposite vertex.

Remember rhombus is a parallelogram (special type) and the four line segments are congruent. A parallelogram has no axis of symmetry where as in rhombus there will be two axis of symmetry.

## Can a Rhombus be a Parallelogram

Rhombus is a parallelogram always as it has two sets of parallel sides but a parallelogram need not be a rhombus. A rhombus should have four sides having equal length. However a parallelogram lacks this feature.

So a rhombus can be a parallelogram but vice-versa is not possible.