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
