The Area of any Irregular Quadrilateral
A plane figure bounded by four straight line segments is called an irregular quadrilateral. The area of any irregular quadrilateral can be calculated by dividing it into triangles.
Example:
Find the area of a quadrilateral whose sides are
m,
m,
m and
m respectively and the angle between the first two sides is a right angle.
Solution:

From the figure we notice that is a right-angled triangle, in which
m,
m. Also
Now, the area of m
In ,
m,
m,
m
m
Now,
The area of the quadrilateral area of
area of
The area of the quadrilateral
square meters.
Example:
In a quadrilateral the diagonal is cm and the two perpendiculars on it from the other vertices are
cm and
cm respectively. Find the area of the quadrilateral.

Solution:
Given that from the figure m,
m,
m
The area of area of
area of
The area of square meters.