Find Area of Parallelogram at Algebra Den

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Home >> Parallelogram >> Area of Parallelogram >>

Find Area of Parallelogram

Area of Parallelogram Opposite Angles of Parallelogram Adjacent Angles of Parallelogram Diagonal Of Parallelogram Difference & Similarity between Rectangle & Parallelogram
Difference & Similarity between Square & Parallelogram Difference & Similarity between Square, Rectangle & Parallelogram Properties of Parallelogram

Before you study how to find area of parallelogram, you are advised to read:

What is a Rectangle ?
How to find Area of Rectangle ?

Formula of finding Area of Parallelogram:
Area of Parallelogram = Base X height or Base X Altitude

In the following diagram:

ABCD is a parallelogram
AB // CD
AD // BC
AD = BC = 3cm
AB = CB = 4 cm
AO = 2 cm

BC is the base of given parallelogram
AO is altitude to side BC

Now let's find the area of this given parallelogram:
Apply above explain formula of area of parallelogram and we get:

Area of Parallelogram = Base X height or Base X Altitude

Since side BC = base and AO = altitude, we get:
Area of Parallelogram ABCD = BC X AO

Put the values of BC and AO from above & we get:
= 3 cm X 2 cm

Solve the multiplication expression and we get:
= 6cm²

Hence, area of parallelogram ABCD = 6cm²

Now let's understand how we got this area formula for parallelogram:

Observe once again the diagram of parallelogram ABCD;

And AO is perpendicular to base BC

Let's cut out the Triangle formed AOB

And move this to the other side i.e. side DC and we get:

And the resultant figure we get

Or on completely joining the side, we get final figure as

Now, you observe that the above figure is a Rectangle ADBO.
And Altitude AO of parallelogram becomes breadth DB of rectangle ADBO
Or we can say that
Altitude 'AO' = Breadth 'DB' ..... (Statement 1)
Similarly Base 'BC' = Length 'OB' ..... (Statement 2)

Hence, from above diagrams, you can understand that:
Area of Parallelogram ABCD = Area of Rectangle ADBO

And since we know that Area of Rectangle ADBO = Length 'OB' X Breadth 'DB', so we get:
Area of Parallelogram = Length 'OB' X Breadth 'DB'

Put the values from statement 1 and 2, we get:
Area of Parallelogram = Base 'BC' X Altitude 'AO'

Therefore this proves that:
Area of Parallelogram = Base X Altitude