Rhombus | what is Rhombus?

Rhombus | what is Rhombus?

Definition: In geometry, a rhombus is a quadrilateral having its all four sides equal.

 

In the given figure of quadrilateral ABCD, AB = BC = CD = AD. So ABCD is a rhombus.

Note:

-          A rhombus is also a parallelogram having its all sides equal.

-          Square is a special case of rhombus having all angles 90°.

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Length of a Rhombus

All four sides of a rhombus are equal and the measure of the side is taken as length (l) of the rhombus. In the given figure of rhombus ABCD,

 

Length of rhombus = AB = BC = CD = AD = l

Diagonals of a Rhombus

The line joining the opposite vertices of a quadrilateral is called a diagonal. Two diagonals of a rhombus bisect to each other at right angle i.e. 90°.

 

In the given figure, ABCD is a rhombus. AC and BD are diagonals. Diagonals AC and BD bisect to each other perpendicularly at point O i.e. OA = OC, OB = OD and ∠COD = ∠BOC = ∠AOB = ∠AOD = 90°

Perimeter and Area of Rhombus

Perimeter and area of a rhombus are given by the formula:

              Perimeter = 4l, where l is the length of the side of rhombus.

              Area = ½ × d₁ × d₂, where d₁ and d₂ two diagonals of rhombus.

Properties of Rhombus

1.       All sides of a rhombus are equal.

2.       Opposite sides of a rhombus are parallel.

3.       Opposite angles of a rhombus are equal

4.       Diagonals of a rhombus bisect each other at right angle.

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