Tutorial Area of a Parallelogram


Area of a Parallelogram


   


A parallelogram is a quadrilateral whose opposite sides are equal length and parallel. The diagonals of a parallelogram are unequal and bisect each other. If is a parallelogram then its area can be calculated in two ways:



(a) When the base and height are given:
Since, is a parallelogram with base, and height,

Area of the parallelogram Area of the rectangle

(as)

Area of parallelogram base height

(b) When adjacent sides and their included angle is given:
Since, is a parallelogram. Take and as its two adjacent sides with included angle .

Area of parallelogram
But
Or
Or
Area of
Area of Parallelogram Product of adjacent sides

Example:
Find the base of a parallelogram whose area is square cm and height cm.
Solution:
Since, area square cm
height cm
Area of parallelogram base height
base
Base cm.

Example:
Find the area of a parallelogram, two adjacent sides of which are cm and cm and their included angle is.
Solution:
Here, one side, cm, other side, cm,
Area


square cm


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