Question

One of the parallel sides of a parallelogram is 22 cm. The distance between the two parallel sides is 18 cm. Find the area of the parallelogram.​

Answer 1

Given the parallelogram ABCD with

AB=24cm and AD=18cm.

Projecting a perpendicular line from vertex A to base DC at point E.

Since

the distance between two lines is the perpendicular distance between them.

And the distance between the longer sides of the parallelogram is given 12cm in the problem.

Hence, AE=12cm

We know that area of the parallelogram is given by

Area = Base x Height

For parallelogram ABCD, Base=AB=CD=24cm, as the opposite sides of a parallelogram are equal. Similarly, Height=AE=12cm.

Therefore, area of parallelogram ABCD =AB×AE = 24×12=288cm

=AB×AE = 24×12=288cm

.

We can also consider the area of the parallelogram ABCD by considering the shorter aside as the base.

Considering the base of the parallelogram ABCD as AD=BC=18cm.

Projecting a perpendicular line from vertex C to base AD at point F, we get Height CF=h cm.

Now again,

Area = Base x Height

⇒288=AD×CF⇒288=18×h⇒h = 28818=16cm

⇒288=AD×CF⇒288=18×h⇒h = 28818=16cm

Hence CF=h=16 cm.

Since the distance between two lines is the perpendicular distance between them.

Distance between the shorter sides of the parallelogram ABCD = CF= 16cm.

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Answer 2

Given the parallelogram ABCD with

AB=24cm and AD=18cm.

Projecting a perpendicular line from vertex A to base DC at point E.

Since

the distance between two lines is the perpendicular distance between them.

And the distance between the longer sides of the parallelogram is given 12cm in the problem.

Hence, AE=12cm

We know that area of the parallelogram is given by

Area = Base x Height

For parallelogram ABCD, Base=AB=CD=24cm, as the opposite sides of a parallelogram are equal. Similarly, Height=AE=12cm.

Therefore, area of parallelogram ABCD =AB×AE = 24×12=288cm

=AB×AE = 24×12=288cm

.

We can also consider the area of the parallelogram ABCD by considering the shorter aside as the base.

Considering the base of the parallelogram ABCD as AD=BC=18cm.

Projecting a perpendicular line from vertex C to base AD at point F, we get Height CF=h cm.

Now again,

Area = Base x Height

⇒288=AD×CF⇒288=18×h⇒h = 28818=16cm

Hence CF=h=16 cm.

Since the distance between two lines is the perpendicular distance between them.

Distance between the shorter sides of the parallelogram ABCD = CF= 16cm.