Perimeter and Area of Rhombus

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

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

Area of a rhombus (A) = $\frac{1}{2}$ (Product of the diagonals)

                                 = $\frac{1}{2}$ × d$_{1}$ × d$_{2}$

Some geometrical properties of a rhombus:

In the rhombus PQRS,

PR ⊥ QS, OP = OR, OQ = OS,

PQ$^{2}$  = OP$^{2}$  + OQ$^{2}$  

QR$^{2}$  = OQ$^{2}$  + OR$^{2}$  

RS$^{2}$  = OR$^{2}$  + OS$^{2}$  

SP$^{2}$  = OS$^{2}$  + OP$^{2}$

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.

Solution:

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

Then, area of the rhombus = $\frac{1}{2}$ × d$_{1}$ × d$_{2}$

                                       = $\frac{1}{2}$ × QS × PR

                                       = $\frac{1}{2}$ × 8 × 6 cm$^{2}$  

                                       = 24 cm$^{2}$  

Now, OP = $\frac{1}{2}$ PR = $\frac{1}{2}$ × 6 cm = 3 cm and,

          OQ = $\frac{1}{2}$ QS = $\frac{1}{2}$ × 8 cm = 4 cm.

Also, ∠POQ = 90°.

So by Pythagoras’ theorem, PQ$^{2}$ = OP$^{2}$  + OQ$^{2}$  

                                                                        = (3$^{2}$ + 4$^{2}$) cm$^{2}$  

                                                                        = (9 + 16) cm$^{2}$  

                                                                        = 25 cm$^{2}$  

Therefore, PQ = 5 cm

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

                                                        = 4 × 5 cm

                                                        = 20 cm

9th Grade Math

From Perimeter and Area of Rhombus to HOME PAGE