Introduction to Rhombus, Area & Its Properties

Introduction to Rhombus

Introduction to Rhombus, AREA & Its properties  In plane geometry, you can say that rhombus is a parallelogram or a simple quadrilateral whose all four sides are equal. Rhombus can also be called as an equilateral quadrilateral, where equilateral means that all of its sides are equal. Here you will learn INTRODUCTION, PROPERTIES & AREA OF RHOMBUS

Type of Rhombus:

Rhombus can be of three types –

Quadrilateral

Parallelogram

Kite

Edges and vertices of a rhombus are four in number. Every rhombus is a parallelogram and a kite and a rhombus with right angles is a square.
If we talk about characteristics of rhombus then, a simple quadrilateral is a rhombus if and only if it possesses any of these characteristics.

1- There must be a quadrilateral in which each and every diagonal bisects two opposite interior angles.
2- There must be a quadrilateral whose diagonals are perpendicular and bisect each other.
3- There must be a quadrilateral with four sides of equal length.
4- There must be a parallelogram in which a diagonal bisects an interior angle.
5- There must be a parallelogram in which at least two consecutive sides are equal in length.

Properties of Rhombus:

There are several basic properties of Rhombus.
1- Every Rhombus has two diagonals connecting pairs of opposite vertices,and the two pairs of parallel sides.
2-Opposite angles of a Rhombus are equal in measure.
3- Diagonals of Rhombus bisects opposite angles.
4- The two diagonals of a Rhombus are always perpendicular.

Here, the very first property states that every Rhombus is a parallelogram, that is, it possesses all of the properties of a parallelogram.

Area & Properties of Rhombus
Properties of rhombus

(4s2=p2+q2)

Where a is the side of rhombus.
p,q is diagonal

But always remember that not every parallelogram is a rhombus or you can say that, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a Kite. Hence, every Rhombus is a kite and my quadrilateral that is both a kite and parallelogram is a rhombus.

Area of Rhombus

Area of Rhombus can be calculated as

1. By taking the altitude times side length of rhombus :

Area = Altitude × side

2. By taking the side lenth squared (s2) times the sine of angle of A (or angle B)

Area = s2 sin (A)
Area = s2 sin (B)

3. By multiplying the lengths of the diagonals and the dividing by 2

Area = 12 x product of diagonals
Area = (p×q)2

The perimeter of Rhombus:

The perimeter of a rhombus can be calculated as :-

Perimeter = s + s + s + s
Perimeter =4s

where ‘s’ is side of rhombus

I hope, this article will help you a lot to understand the Introduction to Rhombus, Area & Its Properties. If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.

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