FINDING AREA AND PERIMETER OF A PARALLELOGRAM

Find the area and perimeter of the following parallelograms :

Problem 1 :

Solution :

From the figure,

Base of a parallelogram (b)  =  11 cm

Height of a parallelogram (h) =  3 cm

Then,

Area of the parallelogram  =  b x h sq. units.

 Area  =  11 x 3

So, area of the parallelogram  =  33 sq. cm.

Perimeter of the parallelogram  =  sum of the length of the four sides.

=  11 cm + 4 cm + 11 cm + 4 cm

So, perimeter of the parallelogram  =  30 cm

Problem 2 :

Solution :                             

From the figure,

Base of a parallelogram (b)  =  7 cm

Height of a parallelogram (h) =  10 cm

Then,

Area of the parallelogram  =  b x h sq. units.

Area  =  7 x 10

So, area of the parallelogram  =  70 sq. cm.

Perimeter of the parallelogram  =  sum of the length of the four sides.

=  13 cm + 7 cm + 13 cm + 7 cm

=  40 cm

Problem 3 :

Find the missing values.

Solution :

(i)

Base of a parallelogram (b)  =  18 cm

Height of a parallelogram (h) =  5 cm

Then,

Area of the parallelogram  =  b x h sq. units.

 Area  =  18 x 5

So, area of the parallelogram  =  90  sq. cm.

(ii)

Base of a parallelogram (b)  =  8 m

Area of the parallelogram  =  56 sq. m

Then,

Area of the parallelogram  =  b x h sq. units.

56  =  8 x h

56/8  =  h

7 m  =  h

So, height of a parallelogram (h)  =  7 m 

(iii)

Height of a parallelogram (h)  =  17 mm

Area of the parallelogram   =  221 sq. mm

Area of the parallelogram  =  b x h sq. units.

221  =  b x 17

221/17  =  b

13 mm  =  b

So, base of a parallelogram (b)  =  13 mm.

Problem 4 :

Suresh won a parallelogram – shaped trophy in a state level chess tournament. He knows that the area of the trophy is 735 sq. cm and its base is 21 cm. what is the height of that trophy?

Solution :

Given,

Base of the trophy (b)  =  21 cm

Area of the trophy   =  735 sq.cm

  Area of the parallelogram  =  b x h sq. units.

735  =  21 x h

735/21  =   h

35 cm  =  h

So, height of trophy (h)  =  35 cm

Problem 5 :

Janaki has a piece of fabric in the shape of a parallelogram. Its height is 12 m and its base is 18 m. She cuts the fabric into four equal parallelograms by cutting the parallel sides through its mid – points. Find the area of each new parallelogram.

Solution :

Given,

Base of a parallelogram (b)  =  18 m

Height of a parallelogram (h)  =  12 m

Area of the parallelogram  =  b x h sq. units.

 =  18 m x 12 m

=  216 m²

Since she cuts the fabric into four equal parallelograms,

=  216/4

 =  54 m²

So, the area of each new parallelogram =  54 m².

Problem 6 :

A ground is in the shape of parallelogram. The height of the parallelogram is 14 meters and the corresponding base is 8 meters longer than its height. Find the cost of levelling the ground at the rate of $ 15 per sq. m.

Solution :

Given,

Base of a parallelogram (b)  =  8 m

Since base is 8 meters longer than height, 

Now, base  =  (14 + 8)  =  22 m

Height of a parallelogram (h)  =  14 m

Area of the parallelogram  =  b x h sq. units.

=  22 m x 14 m

=  308 m²

Cost of levelling 1 m² =  15 per sq. m.

Cost of levelling 308 m²  =  308 x 15

=  $ 4,620

So, the cost of levelling the ground  =  $ 4,620

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