FINDING AREA OF THE RHOMBUS

Formula for finding area of the rhombus :

If the area of the rhombus is in terms of its base and height, we will use to below formula.

Area of the rhombus  =  × h sq.units

Since the rhombus is also like a parallelogram, we can use the same formula to find the area of the parallelogram.

If the area of the rhombus is in terms of its diagonals, we will use to below formula.

Area of the rhombus  = 1/2 × (product of diagonals)

That is,

Area of the rhombus  =  1/2 × d1 × d2 sq. units

Find the area of rhombus PQRS shown in the following figures.

Problem 1 :

Solution :

From the figure,

Given, d1  = 8 cm,  d2  =  16 cm 

Area of the rhombus  =  1/2 x (d1 x d2) sq. units

=  1/2 x (8 cm x 16 cm)

=  1/2 x (128 cm2)

=  64 cm2

Problem 2 :

Solution :

From the figure,

Given,  base =  15 cm , height  =  11 cm

Area of the rhombus  =  b x h sq. units

=  15 cm x 11 cm

=  165 cm2

Problem 3 :

Find the area of a rhombus whose base is 14 cm and height is 9 cm.

Solution :

Given, base (b)   =  14 cm

Height (h)  =  9 cm

Area of the rhombus  =  b x h sq. units

=  14 x 9  =  126

Therefore, area of the rhombus  =  126 sq. cm.

Problem 4 :

Find the missing value. 

Solution :

(i)

Diagonal (d1)  =  19 cm

Diagonal (d2)  =  16 cm

Area of the rhombus  =  1/2 x (d1 x d2)

=  1/2  x (19 cm x 16 cm)

=  1/2 x (304 cm2)

=  152 cm2

Therefore, area of the rhombus  =  152 cm2

(ii)

Diagonal (d1)  =  26 m

Diagonal (d2)  =  ?

Area of the rhombus  =  468 sq. m

Area of the rhombus  =  1/2 x (d1 x d2)

468  =  1/2 x (26 x d2)

468  =  13 x d2

468/13  =  d2

d=  36 m

(iii)

Diagonal (d1)  =  ?

Diagonal (d2)  =  12 mm

Area of the rhombus  =  180 sq. mm

Area of the rhombus  =  1/2 x (d1 x d2)

180  =  1/2 x (d1 x 12)

180  =  d1 x 6

180/6 =  d1

 d = 30 mm 

Problem 5 :

The area of a rhombus is 100 sq. cm and length of one of its diagonals is 8 cm. Find the length of the other diagonal.

Solution :

Given, the length of one diagonal (d1)  =  8 cm

Let, the length of the other diagonal be (d2) cm

Area of the rhombus =  100 sq. cm

Area of the rhombus  =  1/2 x (d1 x d2)

100  =  1/2 x (8 x d2)

100 x 2  =  8 x d2

200  =  8 x d2

200/8  =  d2

25  =  d2

Therefore, the length of the other diagonal is 25 cm.

Problem 6 :

A sweet is in the shape of rhombus whose diagonals are given as 4 cm and 5 cm. The surface of the sweet should be covered by an aluminum foil. Find the cost of aluminum foil used for 400 such sweets at the rate of $ 7 per 100  sq. cm.

Solution :

Given, one diagonal (d1)  =  4 cm

other diagonal (d2)  =  5cm

Area of one rhombus shaped sweet  =  1/2 x (d1 x d2)

=  1/2 x 4 cm x 5 cm

=  10 cm2

Aluminum foil used to cover 400 sweets  =  400 x 10

 =  4000 cm2

Cost of aluminum foil for 100 cm=  $7

Cost of aluminum foil for 4000 cm2  =  (4000/100) x 7

=  $ 280

Therefore, the cost of aluminum foil used  =  $ 280.

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