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Area of rhombus


To show that the area of rhombus is half the product of its diagonals.


  1. A rhombus is a simple (non-self-intersecting) quadrilateral whose all four sides are of same length.
  2. If a parallelogram has two consecutive sides congruent, it is a rhombus.
  3. If two triangles are congruent then their areas are equal.
  4. Area of a triangle = 1/2 X base X height
  5. Area of a rectangle = Length X Breadth
  6. Diagonals of rhombus are perpendicular to each other.


In above figure EHGF is rhombus with diagonal HF (length d1) and diagonal EG (length d2)

Area of rhombus EHGF = Area of triangle EFH + Area of triangle FHG
                      small = frac{1}{2} 	imes EO 	imes HF + frac{1}{2} 	imes HF 	imes OG

                      small =frac{1}{2} 	imes (frac{d2}{2}) 	imes d1+frac{1}{2} 	imes (frac{d2}{2}) 	imes d1

                      small =frac{(d1	imes d2)}{4}+frac{(d1	imes d2)}{4}
                      small =frac{2(d1 	imes d2))}{4}

                      small =frac{d1 	imes d2}{2}
                      = half of the product of the diagonals


Find the area of the following rhombus.


In the given figure,

PR = d1= 24 cm.

SQ = d2 = 18 cm.


So, the area of the rhombus PQRS is 216 cm2.