# Rhombus -Properties ,Area ,Perimeter and Shape

 Rhombus -Properties ,Area ,Perimeter and Shape

## Shape of Rhombus

Rhombus   is two dimensional figure with four equal sides and opposite sides are parallel     . Opposite angles are equal . Two diagonals are not in equal length but bisect each other at 90°.

## What is Rhombus ?

Rhombus is a  type of Quadrilateral, means which has four sides and all four sides are equal. If all the    sides of a Parallelogram are equal ,it is called a Rhombus .

## Properties of Rhombus

Properties of Rhombus are listed below.
• A rhombus is  a quadrilateral, which means it has four sides and each of these sides are congruent.
• The opposite sides  are parallel to each other of a rhombus.
•  The opposite angles  of a rhombus  are congruent.
• The diagonals of a rhombus are perpendicular.
• The diagonals  form four congruent interior triangles in  a rhombus.
• The diagonals of a rhombus  bisect each other.
• A rhombus has all the properties of parallelogram.
•                                  1.Opposite sides are congruent.
2.The opposite angles are congruent.
3.The diagonals  bisect each other.

• All squares are Rhombus but not all rhombuses are squares.
• The diagonals of a rhombus do not have the same length.
• Diagonals are angle bisector.
• Consecutive angles are supplementary.

## Area of Rhombus

If d1 and d2 be the diagonals of a Rhombus,

We have  Formula for Area = 1/2*d1*d2.

Example:-Find the area of a rhombus whose diagonals are 6cm and 8cm respectively.

Answer:  According to formula area =1/2*d₁*d₂.

d₁=6cm
d₂=8cm
area=1/2*d₁*d₂.
= 1/2*6*8cm

=24cm².

## Perimeter of Rhombus

Perimeter is the continuous line forming the boundary of a closed geometrical figure.
Here perimeter is region surrounded by the four sides of the rhombus.
Perimeter= 4* side.

Example:-Find the perimeter of a rhombus whose diagonals are 6cm and 8cm respectively.

Answer:  We know diagonals of a rhombus bisect each other and the diagonals of
 Rhombus -Properties ,Area ,Perimeter and Shape

rhombus are perpendicular.
Here we can  apply the Pythagoras  theorem to find the side of rhombus.

According to Pythagoras theorem

AB²= AO²+BO²
AB²= 3²+4²
AB²= 9+ 16
AB²= 25
AB= 5
We know  Perimeter of rhombus = 4* side of the Rhombus
=4*5
= 20 cm.
2. Square

## FAQs

1.Area of a rhombus is 42m2 one of its diagonal is 7 cm find the length of the second diagonal.
Ans – As we know the formula for rhombus is = 1/2*product of diagonals.
here area  and length of one diagonal is given
Area=1/2*d1 *d2    (d1 and d2 are two diagonals)
42cm²= 1/2*7*d2
42*2=7d2
84/7=d2
12= d2
12cm is the length of the second diagonal
2. The area of rhombus whose diagonals are 7.5cm and 5.6cm respectively is

Ans-Here two diagonals are given .According to area formula
Area= 1/2*7.5cm*5.6 cm
Area=21cm².
3.If one angle of rhombus is 144 then other angles is

Ans  –As we know the opposite angles  of a rhombus  are congruent ,and Consecutive angles are supplementary.

if one angle is 144 then other angle is= 180°-144°
=36°

4.What is a rhombus in math?
Ans-Rhombus is a two dimensional figure having four equal sides and opposite sides are parallel .Two diagonals bisect  and  perpendicular to each other.

5.Is a square a rhombus?
Ans-yes, every square is  a rhombus but vice versa is not true.