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Formula to Find Height of a Rhombus

Rhombus:
A parallelogram in which all four sides are equals called a rhombus. In rhombus ABCD shown in the figure AB = BC = CD = DA and AB is parallel to CD and BC is parallel to AD. 


A Parallelogram

Properties of Rhombus:
         All the sides are equal.
         Opposite angles are equal
         Diagonal bisect each other at an angle of 90º


Area of Rhombus:
Rhombus is similar to a parallelogram. The sides of a rhombus remains same.
The area can be found by :


Area of Rhombus


  • When Diagonals are given:
                     The area of rhombus (A) = $\frac{d_{1}d_{2}}{2}$
  • When base and height of Rhombus is known:


A Rhombus

                      The area of rhombus (A) = b x h 
                      where b is base and h is height of  a rhombus.

Height of a Rhombus:
Height of Rhombus can be found when the area and base of rhombus is known.

Formula for height of rhombus:
We have area of rhombus A = base x height

           $\frac{Area}{base}$ = height


Example Problems:

           1. Find the height of Rhombus when the area is 54 cm2 and height 6 cm.

Solution:  We have area of Rhombus = base x height

                         Height = $\frac{Area}{base}$

                                   = $\frac{54}{6}$

                                   =  9 cm.

                         Height of rhombus is 9 cm.


            2. The diagonal of Rhombus are 6 cm and 8 cm with base 4 cm. Find the height of the rhombus.

  Solution:  Given the diagonals of rhombus  d1 and d2 are 6 cm and 8 cm.

                  Area of rhombus when diagonals are known: A = $\frac{d_{1}d_{2}}{2}$

                                                                    = $\frac{6*8}{2}$

                                                                    = $\frac{48}{2}$ = 24 cm2

                 Height of Rhombus ; h = $\frac{Area}{base}$

                                                  = $\frac{24}{4}$

                                                  = 6 cm.

                Height of rhombus is 6 cm.