Perimeter of Rhombus

In this page perimeter of rhombus we are going to see formulas to be used to find the perimeter of the shape rhombus. We have two methods to find the perimeter-of-rhombus. We can use any formula depending on the information given in the question.

Formula:

Perimeter-of-rhombus = 2 √ d₁² + d₂²

(or)

4a


Now we are going to see some examples problems where we have to apply these two methods.

Example 1:

Find the length of the other diagonal and area of rhombus.If the perimeter of a rhombus is 20 cm and One of the diagonals is of length 8 cm.

Solution:

Since one of the diagonal is given and we have to find the other diagonal. So we have to use the first formula.

Perimeter of the rhombus = 2 √ d₁² + d₂²

Here d₁ = 8 cm

Perimeter of the rhombus = 20 cm

                 2 √8² + d₂² = 20

                   √64 + d₂² = 20/2                   

                    64 + d₂² = (10)²

                    64 + d₂² = 100                 

                          d₂² = 100 - 64

                          d₂² = 36

                          d₂ = √36

                          d₂ = √6 x 6

                          d₂ = 6 cm

So area of rhombus = (1/2) x 8 x 6

                          = 4 x 6

                         = 24 cm²

Example 2:

Find the length of each side of rhombus if the perimeter is measuring 260 cm.

Solution:

Perimeter of the rhombus = 260 cm

                              4a = 260 m

                                a = 260/4

                                a = 65 cm

Example 3:

Find the perimeter of the rhombus whose vertices are A (2,-3), B (6,5), C (-2,1) and D (-6,-7).

Solution:

To find the perimeter 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

Perimeter of rhombus = 2 √ (√41)² + √288)²)

                             = 2 √ 41 + 288

                             = 2 √329 cm

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Perimeter of Rhombus to Formulas for Shapes