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Finding the area of ​​any shape of land:-

Let ABCDEF be a plot of arbitrary shape.  To determine the area of ​​such uneven shaped land, the land must first be divided some triangles.Find the area of ​​a triangle by measuring the length of its perimeter using the following formula.  The formula is:-

 Area(∆)=√s(s-a)(s-b)(s-c),( here S=a+b+c/2.)

A,B,and C are the lengths of the three sides of the triangle.  Area of ​​ABCDEF=∆1+∆2+∆3+∆4.    

■ Determining the area of ​​the curve:- 

If the boundary of a land is curved, divide the land in  some triangles and then find the area of ​​the additional part of the land without the triangle (the part indicated by the diagonal line in the sign) by the following methods...      

(1)Mid Ordinate Method:- 

In this method the field is to be divided into parts of equal width, let the width of each part be H. Now find the length along the midpoint of the parts.

 Let's say, the segments are h1, h2, h3, h4, h5, h6 . Therefore the area of ​​the defined area is the sum of the areas of each segment.Therefore, ABCD is the area of ​​triangle - 

=dh1+dh2+dh3+dh4+dh5+dh6                         =d(h1+h2+h3+h4+h5+h6) square unit.  

Thus if the part is divided into n number of parts, the area will be determined,

 =( square unit.   

  2) Arrange Ordinate rule:- 

In this method the land of the field should be divided into equal number of lengths.  Find the length by drawing a perpendicular from each segment. 

The lengths are O0,O1,O2,O3....On 

Therefore, the area of ​​the field will be ∆=O0+O1+O2+.....On/n+1×d.   

Where O0,O1,O2,O3 ....On is the length of n number of drawn perpendiculars. 

 d = Land length of land segment.

n = Land divided into n number of segments.


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