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activity
Take a cardsheet and draw a parallelogram shape on it and cut out the parallelogram from the sheet.
Now, cut the parallelogram into pieces along its base as shown in the below figure and rearrange them to form
a rectangle.
Height
Height

Base Base
Clearly, area of the parallelogram = Area of the rectangle formed
= length × breadth

Note: The perpendicular dropped on that side from the opposite vertex is known as height (altitude).

Here, length and breadth of the rectangle are the base and
height of the parallelogram, respectively.

So, Area of a parallelogram = base × height
If b and h be the base and height of the parallelogram,
respectively. Side (a) Height (h)
Thus, the area of the parallelogram = b × h sq. units
Base (b)
Also, perimeter of a parallelogram = 2 (side + base) units

Any side of a parallelogram can be chosen as base of the parallelogram and we can draw
perpendicular from any vertex of the parallelogram.
In the fig(i), parallelogram ABCD, BF is the perpendicular to opposite side AD. So, AD is the base

and BF is the height.
And in fig(ii), DE is the height and AB is the base of parallelogram ABCD.

D C
D C

F
Height
Base
A B A E B
Height Base
Fig (i) Fig (ii)
Example 11: Find the perimeter and area of the adjoining figure of parallelogram.
Solution: Given, base = length = 7 cm, height = 6 cm, and breadth = side = 5 cm

Perimeter of a parallelogram = 2(side + base)
= 2 × (5 + 7) cm 6 cm 5 cm

= 2 × 12 cm = 24 cm
7 cm
Also, Area of the parallelogram = base × height
= 7 cm × 6 cm = 42 cm 2

Mathematics-7 288