AREA OF RHOMBUS
About "Area of a rhombus"
Area of rhombus :
Here we are going to see the formula to be used to find area of rhombus and some example problems.
Definition of rhombus
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.
- Properties of rhombus:
- It has four equal sides
- Both diagonals are intersecting each other at right angle.
- Opposite angles are congruent in a rhombus.
- Sum of interior angles will be 360 degree
Difference between square and rhombus:
SquareEach corner is measuring 90°. Lengths of diagonals are equal. The midpoint of diagonals of square are not equal |
RhombusEach corner is not measuring 90°. Lengths of diagonals are not equal. The midpoint of diagonals of rhombus are equal |
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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