Rhombus -Properties ,Area ,Perimeter and Shape

                                Rhombus -Properties ,Area ,Perimeter and Shape

Rhombus -Properties ,Area ,Perimeter and Shape
Rhombus -Properties ,Area ,Perimeter and Shape

     In this article  we will cover the topics listed below.  

  1.Shape of Rhombus

  2. Properties of Rhombus     

  3. Area of Rhombus    

  4. Perimeter of Rhombus   

  5.  Frequently Asked Questions on Rhombus                                                                                                                                                                                    

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.
                     = 1/2*6*8cm


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 -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
                                            = 20 cm.
Related Topics to read
    2. Square


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
           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
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°

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.

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