On the webpage, we are going to see the formula to be used to find area of rhombus and some example problems.
A quadrilateral which is having four equal sides is called rhombus. In other words a parallelogram will become rhombus if the diagonals are perpendicular.
Area of rhombus = (1/2) x (d₁ x d₂)
Here d₁ and d₂ are diagonals.
Square

Rhombus

Example 1:
Find the area of rhombus if the diagonal is measuring 15 cm and 10 cm.
Solution:
Here d₁ = 15 cm d₂ = 10 cm
Area of the rhombus = (1/2) x (d₁ x d₂)
= (1/2) x 15 x 10
= 15 x 5
= 75 cm²
Example 2:
Find the area of the rhombus whose vertices are A (2,3), B (6,5), C (2,1) and D (6,7).
Solution:
To find the area of the rhombus first we have to find the length of the diagonals.
Distance between two points = √(x₂  x₁)² + (y₂  y₁)²
Length of diagonal AC :
A (2,3) C (2,1)
x₁ = 2 , y₁ = 3 , x₂ = 3 , y₂ = 1
= √(3  2)² + (1  (3))² ==> √25 + (4))² ==> √(25 + 16) ==> √41
Length of diagonal BD :
B (6,5) D (6,7)
x₁ = 6 , y₁ = 5 , x₂ = 6 , y₂ = 7
= √(6  6)² + (7  5)² ==> √(12)² + (12)² ==> √144 + 144
= √288 ==> √12 x 12 x 2 ==> 2√12
Area of the rhombus = (1/2) x (d₁ x d₂)
d₁ = √41 d₂ = 2√12
= (1/2) x √41 x 2√12
= √41 x √12
= √12 x 41
= √492
= √2 x 2 x 3 x 41
= 2 √123 square units
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