## 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

# Square

Each corner is measuring 90°.

Lengths of diagonals are equal.

The midpoint of diagonals of square are not equal

# Rhombus

Each 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

After having gone through the stuff given above, we hope that the students would have understood "Area of a rhombus"

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## More shapes

 Square Parallelogram Rectangle Rhombus Traingle Quadrilateral Area of quadrilateral Sector Hollow cylinder Sphere Area around circle Area around circle example problems Area of combined figures Example problems of area of combined figures Trapezium Area of trapezium Circle Semicircle Quadrant Example problems on quadrant Cyclinder Examples problems of cylinder Cone Hemisphere Example problems of hemisphere Path ways Area of path ways

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