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Perimeter and Area of Rhombus

Here we will discuss about the perimeter and area of a rhombus and some of its geometrical properties.

Perimeter and Area of Rhombus

Perimeter of a rhombus (P) = 4 × side = 4a

Area of a rhombus (A) = 12 (Product of the diagonals)

                                 = 12 × d1 × d2

Some geometrical properties of a rhombus:

In the rhombus PQRS,

PR QS, OP = OR, OQ = OS,

PQ2  = OP2  + OQ2  

QR2  = OQ2  + OR2  

RS2  = OR2  + OS2  

SP2  = OS2  + OP2


Solved Example Problem on Perimeter and Area of Rhombus:

1. The diagonals of a rhombus measure 8 cm and 6 cm. Find the area and the perimeter of the rhombus.

Problem on Perimeter and Area of Rhombus

Solution:

In the rhombus PQRS, QS = 8 cm and PR = 6 cm.

Then, area of the rhombus = 12 × d1 × d2

                                       = 12 × QS × PR

                                       = 12 × 8 × 6 cm2  

                                       = 24 cm2  

Now, OP = 12 PR = 12 × 6 cm = 3 cm and,

          OQ = 12 QS = 12 × 8 cm = 4 cm.

Also, ∠POQ = 90°.

So by Pythagoras’ theorem, PQ2 = OP2  + OQ2  

                                                                        = (32 + 42) cm2  

                                                                        = (9 + 16) cm2  

                                                                        = 25 cm2  

Therefore, PQ = 5 cm

Therefore, perimeter of a rhombus (P) = 4 × side

                                                        = 4 × 5 cm

                                                        = 20 cm





9th Grade Math

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