Rhombus -Properties ,Area ,Perimeter and Shape

Rhombus -Properties ,Area ,Perimeter and Shape

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

• 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

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

a 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.

Related Topics to read

   1.Rectangle

    2. Square

    3.Trapezium

   4. Type Of Quadrilateral

   

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