Perimeter of a Rhombus with Diagonals

Normally rhombus is one of the quadrilateral which are having equal length in four sides.  In this two diagonals of a rhombus are bisect each other at 90 degree right angle. Another name of the rhombus is diamond. Because this s having diamond shape. Perimeter is nothing but the path surrounded by some area. So we have to find the path length for that we have to add all the sides of the geometry figure.

 

Example Problems for Perimeter of a Rhombus with Diagonals:

 

Let us take a sample rhombus figure. From the figure we can understand there are four right angles. Their diagonals not equal. But each triangle is having the half of the diagonal length as side length.  From that using Pythagorean Theorem we can find the side length of the rhombus. Here we will see some example for finding the perimeter of a rhombus with diagonals.

 

Perimeter of rhombus with diagonal - rhombus

Example 1 perimeter of a rhombus with diagonals:

 

The two Diagonal lengths of a rhombus are 12 cm and 16 cm. Find the perimeter of the given rhombus.

Solution:

                First we have to draw the rhombus figure.

Perimeter of rhombus with diagonal - 1

                From that we have to take any one of the right angle triangle which is having the side length is 6 cm and 8 cm.

                Using the Pythagorean Theorem we can find the other side length. That is the side length of the rhombus.

                         h = sqrt(8^2 + 6^2)

                         h= sqrt(64 + 36)

                         h = sqrt (100)

                         h = 10 cm. so the side length of rhombus is 10 cm.

               From that perimeter of a rhombus = 10 + 10 +10 +10 = 40 cm.

 

Example 2 for Perimeter of a Rhombus with Diagonals:

 

                Find the perimeter of the given rhombus.

Perimeter of rhombus with diagonal - 2

Solution:

                 From the diagram the side length of the rhombus = h = sqrt(3^2 + 4^2)

                                                                                                               h = sqrt (9 + 16)

                                                                                                                h = sqrt (25)

                                                                                                                h = 5

                   Using this we can find the perimeter of the rhombus.

                    We know perimeter of a rhombus = sum of all sides

                    So perimeter of the rhombus = 5 + 5 + 5 + 5 = 20 cm.

                From the above we can understand how to find the perimeter of a rhombus with diagonals.