Let there be n sides of the polygon. Then it has n vertices.
The total number of straight lines obtained by joining n vertices by talking 2 at a time is ⁿC₂
These ⁿC₂ lines also include n sides of polygon.
Therefore, the number of diagonals formed is ⁿC₂ - n.
Thus, ⁿC₂ - n = 44
? [n(n - 1)/2] - n = 44
? ( n² - 3n) / 2 = 44
? n² - 3n = 88
? n² - 3n - 88 = 0
?(n - 11) (n + 8) = 0
? n = 11

Let the radius of circle is 'r' and a side of a square is 'a',
then given condition
2?r = 4a
? a = ?r/2

? Area of square = (?r/2)² = ?² /4r² = 9.86r²/4 = 2.46r²
and area of circle = ?r² = 3.14;r²
and let the side of equilateral triangle is x.
Then, given condition,
3x = 2?r
? x = 2?r/3

? Area of equilateral triangle = ?3/4 x ²
= ?3/4 x 4?²r²/9
= ?²/3?3r²
= 1.89r²

Hence, Area of circle > Area of square > Area of equilateral triangle.

let each side of the square be a , then area = a 2 

As given that The side is increased by 25%, then 

New side = 125a/100 = 5a/4 

New area =  5 a 4 2  

Increased area=  25 a 2 16 - a 2 

Increase %= 9 a 2 / 16 a 2 * 100  % = 56.25%

let length = x and breadth = y then  

2(x+y) = 46         =>   x+y = 23  

x²+y² = 17² = 289  

now (x+y)² = 23² 

=> x²+y²+2xy= 529 

=> 289+ 2xy = 529

=> xy = 120  

area = xy = 120 sq.cm

Let original radius = R. 

New radius =  50 100 R=  50 100 R 

Original area = R 2  and new area =  ?R 2

3 ?R 2 4 * 1 ?R 2 * 100 

Decrease in area =  ? R 2 2 = ?R 2 4 = 75%

l 2 + b 2 = 41 (or)    l 2 + b 2 = 41  

Also,  l b = 20

l + b 2 = l 2 + b 2 + 2 l b  = 41 + 40 = 81

(l + b) = 9. 

Perimeter = 2(l + b) = 18 cm.

let ABCD be the given parallelogram 

area of parallelogram ABCD = 2 x (area of triangle ABC) 

now a = 30m, b = 14m and c = 40m

 s=1/2 x (30+14+40) = 42 

Area of triangle ABC =  s s - a s - b s - c  

= 42 12 28 2= 168sq m 

area of parallelogram ABCD = 2 x 168 = 336 sq m

Let original length = x metres and original breadth = y metres.

Original area = xy sq.m 

Increased length  =  120 100 and Increased breadth =  120 100 

New area =  120 100 x * 120 100 y = 36 25 x y m 2 

The difference between the Original area  and New area  is:  

36 25 x y - x y

11 25 x y Increase % = 11 25 x y x y * 100= 44%

Let the side of the square(ABCD) be x meters.

Then, AB + BC = 2x metres.

AC =  2 x = (1.41x) m.

Saving on 2x metres = (0.59x) m.

Saving % = 0 . 59 x 2 x * 100 = 30% (approx)

Let the side of the square be x. Then, its diagonal =  2 x 2 = 2 x 

Radius of incircle =  x 2 

Radius of circum circle=  2 × x 2 = x 2 

Required ratio =  ?x 2 4 : ?x 2 2 = 1 4 : 1 2 = 1 : 2