maneesh dhauni 

Introduction :

The idea to increase the current land twice or four
times for use of construction or agriculture. Procedure :

Current state:

1. Let the current land area be determined as follows –Length =a units and breadth= b
   units.
2. Total area of the current land = a X b= (Area-Current) units.

Modified state:

1. Drawline mid of land in east west direction –as sun rise in the east and set in the
   west. For Agriculture this is helpful.  Length
   of mid line = half of length units= a/2 units.
2. Frommid point, let construct triangle of height c units. Let the length from tip of
   triangle to surface end be denoted by d unit. 
   So length of d is determine by Pythagorean theorem.
3. The Pythagorean Theorem
   states that for any right triangle the square of the hypotenuse equals the sum
   of the squares of the other 2 sides.
4. Here in present case-If we draw a
   right triangle having sides 'c' 'a/2' and 'd' (with 'd' being the hypotenuse) then according to the theorem, the length of d² = a/2² + c²
5. Hence, we construct isosceles
   triangular prism on our land as shown in the Fig 2. This isosceles triangular
   has two rectangles with breadth b  units
   and length d units
6. Now the surface area of one side of
   isosceles triangular prism is equal to sum of area of two rectangles. b X d + bX d= 2( b X d) units = Modified area
7.  Now square modified area= [2( b Xd)] ²=4b²d².
8. Square Modified area =4b²( a/2² + c²)………….from
   point 6 above.
9. Square Modified area= b²a²+4b²c².=(Area-Current)² +4b²c.
10. Let a=b=c=1 unit.
11. Square modified area = (1 X 1) ² +4 (1) ²X 1=1+4=5
12. So modified area = square root of 5=2.236=2.24 units square.
13. Hence modified area is increase by 2.24 units square.
14. In case we make two isosceles triangles build in the current land surface, than area shall increase 2 X 2.24= 4.48.