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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  ,  ,  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, Area of  m
In  ,  m,  m,  m
 m
Now, Area of 
 Square meter
Area of Quadrilateral   Area of   Area of 
 Square meter
 Square meter
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
Area of  Area of  Area of 
 Square meter
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