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.

Area of equilateral triangle = ?3a²/4 = x ......(i)

And perimeter = 3a = y
? a = y/3 ....(ii)

Now, Putting the value of a from Eq. (ii) in Eq. (i). we get
?3 (y/3)²/4 = x
? x = ?3 x y²/36
? x = y²/3?3x = y²/12?3
12?3 x = y²
On squaring both sides, we get
y⁴ = 432x²

We know that, the radius of a circle inscribed in a equilateral triangle = a/[2?3]
Where, a be the length of the side of an equilateral triangle.

Given that, area of a circle inscribed in an equilateral tringle = 154 cm²
? ?(a/2?3)² = 154
? (a/2?3)² = 154 x (7/22) = (7)a²
? a = 42?3 cm

Perimeter of an equilateral triangle = 3a
= 3(14?3)
= 42?3 cm

Given that, l = 2b [Here l = length and b = breadth]

Decrease in length = Half of the 10 cm = 10/2 = 5 cm
Increase in breadth = Half of the 10 cm = 10/2 = 5 cm
Increase in the area = (70 + 5) = 75 sq cm

According to the question,
(l - 5) (b + 5) = lb + 75
? (2b - 5) (b + 5) = 2b² + 75 [since l = 2b]
? 5b - 25 = 75
? 5b = 100
? b = 100/ 5 = 20
? l = 2b = 2 x 20 = 40 cm

Area of square = (Side)² = 20²
= 400 sq cm

? Area of rectangle
= 1.8 x 400 = 720 sq cm

Let length and breadth of rectangle be 5k and k respectively.
Then, according to the question,
5k x k = 720
? 5k² = 720
? k² = 720/5 = 144
? k = ?144 = 12 cm

Perimeter of rectangle = 2(5k + k) = 12k
= 12 x12 = 144 cm

Area of square plate = (Side)²
= (2d)²
= 4d²

Area of circular plate = ? (d/2)²
= ?d²/4

? Number of square plates
= [(4d²)/4] / [(?d²)/4]
= (4 x 4)/?
? 5
Since, nearest integer value is 5.

Let one diagonal be k.
Then, other diagonal = (60k/100) = 3k/5 cm
Area of rhombus =(1/2) x k x (3k/5) = (3/10)
= 3/10 (square of longer diagonal)
Hence, area of rhombus is 3/10 times.

Let each side of the square be a. Then, area = . a 2
New side = 125 a 100 = 5 a 4. New area =  5 a 4 2 =  25 a 2 16

Increase in area =  25 a 2 16 - a 2 = 9 a 2 16
Increase% =  9 a 2 16 * 1 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 and  new radius = (50/100) r = r/2

original area =  ?r 2 and new area =  ? r / 2 2

decrease in area =  3 ?r 2 / 4* 1 ?r 2 *100 = 75%