AREA OF PARALLELOGRAM

In this page area of parallelogram we are going to see how to find the area of any parallelogram.

Definition of parallelogram:

A parallelogram is a quadrilateral in which opposite sides are parallel and equal in length. In other words opposite sides of a quadrilateral are equal in length,then the quadrilateral is called a parallelogram.

Properties of a parallelogram:

(i) Opposite sides are equal.

(ii) Opposite sides are parallel.

(iii) The diagonal of the parallelogram bisect each other.

(iv) The midpoint of the diagonals will be equal.

(v) Opposite angles of a parallelogram are equal.

The formula to find area of a parallelogram:

Area = b x h

Now let us see example problems to understand this topic much better.

Example 1 :

Find the area of a parallelogram if the base is measuring 15 cm and the height is measuring 3 cm.

Solution:

Area of a parallelogram = b x h

base = 15 cm and height = 3 cm

Area of a parallelogram =  15 x 3

 =  45 cm²

Example 2 :

Find the base of a parallelogram if its area is 40 cm² and its altitude is 15 cm.

Solution:

Area of a parallelogram  = 40 cm²

b x h  =  40 cm²

Here altitude (or) height = 15 cm

b x 15 = 40  ==> b = 2.67 cm

Example 3 :

Find the height of a parallelogram if its area is 612 cm² and its base is 18 cm.

Solution:

Area of a parallelogram  = 612 cm²

b x h = 612 cm²

base = 18 cm

18 x h  = 612 ==>  h =  34 cm

Example 4 :

Find the area of parallelogram in meters. If the base is measuring 100 cm and the height is measuring 12 cm.

Solution:

Area of a parallelogram = b x h

Base  =  100 cm , height  =  12 cm

Area of a parallelogram  =  100 x 12

=  1200 cm² ==> 1 m  =  100 cm ==> =  1200/100 ==> =  12 m²

Hence, area of parallelogram is 12 m²

Example 5 :

A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is :

Solution:

A triangle and a parallelogram which are lying on the same base and between the same parallels are equal in area.

Let h₁ and h₂ are heights of triangle and parallelogram respectively.

So, area of triangle  =  area of parallelogram

(1/2) x b h₁  =  b x h₂

altitude of parallelogram (h₂)  =  100 m

h₁  =  2 h₂ ==> h₁  =  2 (100)  ==> 200 m

Hence, height of parallelogram is 200 m.

Example 6 :

A parallelogram has sides 30 m and 14 m and one of its diagonals is 40 m long. Then, its area is :

Solution:

A triangle and a parallelogram which are lying on the same base and between the same parallels are equal in area.

Area of parallelogram ABCD = 2 x area of triangle ABC

Since, triangle ABC is a isosceles triangle

Area of triangle ABC  =  √s (s - a)(s - b)(s - c)

s  =  (a + b + c)/2

s  =  (30 + 14 + 40) / 2 ==> 84/2 ==> 42

s - a = 42 - 30 = 12

s - b = 42 - 14 = 28

s - c = 42 - 40 = 2

 =  √s (s - a)(s - b)(s - c)

=  √42 x 12 x 28 x 2

=  168 m²

Area of parallelogram ABCD = 2 x 168 = 336 m²

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