Objective
To show that the area of rhombus is half the product of its diagonals.
Theory
A rhombus is a simple (non-self-intersecting) quadrilateral whose all four sides are of same length.
If a parallelogram has two consecutive sides congruent, it is a rhombus.
If two triangles are congruent then their areas are equal.
Area of a triangle = 1/2 X base X height
Area of a rectangle = Length X Breadth
Proof
In above figure EHGF is rhombus with diagonal HF (length d_{1)} and diagonal EG (length d_{2)}
Area of rhombus EHGF = Area of triangle EFH + Area of triangle FH
= half of the product of the diagonals
Example
Find the area of the following rhombus.
Solution:
In the given figure,
PR = d_{1}= 24 cm.
SQ = d_{2 }= 18 cm.
So, the area of the rhombus PQRS is 216 cm^{2}.