Area of Rhombus

In this page area of rhombus we are going to see formula to be used to find area-of-any-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.

Formula:

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 

Now let us see the difference between square and rhombus:

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-the-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

                            =  √(-5)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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Area of Rhombus to Formulas for Shapes