PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

Book Free Demo
We know that a quadrilateral is made up of four sides. Any quadrilateral can be divided into two triangles with the help of a diagonal. This process of dividing a quadrilateral into triangles is called triangulation.
 
Let us look at the figure given below to know how a quadrilateral would look like after triangulation.
 
1.PNG
 
Here, \triangle ABD and \triangle BCD are formed after triangulation.
 
To find the area of the quadrilateral, we should know the values of h_1 and h_2. h_1 and h_2 are the perpendiculars drawn from the diagonal to the vertices. Let us look at the figure given below for a better understanding.
 
2.PNG
 
From the figure given above, we can come to the following inferences.
 
ABCD is a quadrilateral with d as the diagonal and h_1 and h_2 as its heights.
  
\text{Area of quadrilateral} ABCD = (\text{Area of} \triangle ABD) + (\text{Area of} \triangle BCD)
 
[Since the diagonal is divided into two triangles after triangulation]
 
= (\frac{1}{2} \times BD \times h_1) + (\frac{1}{2} \times BD \times h_2)
 
[Since,\text{Area of a triangle}= \frac{1}{2} \times b \times h,where b and h are its base and height respectively]
 
= \frac{1}{2} \times BD \times (h_1 + h_2)
 
= \frac{1}{2} \times d \times (h_1 + h_2)
 
Therefore, \text{Area of a quadrilateral} = \frac{1}{2}d(h1 + h2) square units.