Introduction :

The idea to increase the current land twice or four

times for use of construction or agriculture. Procedure :

Current state:

- Let the current land area be determined as follows –Length =a units and breadth= b

units. - Total area of the current land = a X b= (Area-Current) units.

Modified state:

- 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. - 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. - 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. - 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 - 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 - 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 - Now square modified area= [2( b Xd)] ²=4b²d².
- Square Modified area =4b²( a/2² + c²)………….from

point 6 above. - Square Modified area= b²a²+4b²c².=(Area-Current)² +4b²c.
- Let a=b=c=1 unit.
- Square modified area = (1 X 1) ² +4 (1) ²X 1=1+4=5
- So modified area = square root of 5=2.236=2.24 units square.
- Hence modified area is increase by 2.24 units square.
- In case we make two isosceles triangles build in the current land surface, than area shall increase 2 X 2.24= 4.48.