When d1 and d2 are the diagonals of rhombus then,
The Side of rhombus = Area Aptitude

Area Aptitude

Squaring both sides

202 = 16^2 + d2^2

400 = 256 + d2^2

d2^2 = 400 - 256

d2 = √144

d2 = 12

Area of rhombus =1/2( d1 × d2 )

 =1/2 ( 16 × 12 )=96 cm^2

Triangle area = 12 * base * height
As a result, the area is 12 * 5 * 10 = 25 square metres.

Let each side of the square be X. Then, area = X^2.
New side =(116X/100) =(29X/25). New area = (29X/25)^2
Increase in area = (29X/25)^2 - X^2 =841/625X^2 - X^2=216/625X^2
⇒ Increase% = [(216/625X^2x1/(X^2))*100] % = 34.56%.

Let the length of the rectangle be 'x' and breadth of the rectangle be 'y'

According to the question:

2(x + y) - x = 100

2x + 2y - x = 100

x + 2y = 100

From this we cannot find 'y' (breadth), so the given data is inadequate.

Let the breath = x

So, the Length = 3x

Perimeter of a rectangle = 2 (Length + Breadth)
So, 2 (3x + x) = 106
      6x + 2x = 106
      8x = 106
       x = 104/8 = 13

Now, Breadth = 13, so, length = 13 * 3 = 39

So, its area = Length * Breadth
                     = 39 * 13 = 507 sq. m.

 
The area of a right angled triangle = ½ * base * height

Base = 10, Hypotenuse = 20

Height2 = Hypotenuse2 - Base2 
          = 202 - 162
          = 400 - 256
Height2  = 144
Height  = 12

Area = ½ * base * height
           = ½ * 10 * 12
          = 60 meters

Area of a square = 1/2 (diagonal) 2

                = 1/2 (40)2

                = 1/2 * 1600

                = 800 sq. m.

 
Perimeter of a rectangle = 2 (Length + Breadth)

Let length is L and breadth is B.

So, as per the question = 2(L+B)/B = 10/2
                                     2(L+B)/B = 5/1
                                     2L + 2B = 5B
                                     2B - 5B = - 2L
                                     - 3B = - 2L
                                     B = 2/3 L

Given Area = 430 sq. cm.

Area = Length * Breadth
         430 = L * 2/3 L
         430 = 2/3 L2

Or L2 = 1290 / 2
  L2 = 645
   L = 25.4 cm
 

One round of the park is equal to the perimeter of the park.

So, by completing one round, the cat covers a distance equal to the perimeter of the park.

Now, Distance or perimeter = speed * time
                                            = 18 * (10/60)
                                            = 3 km or 3000 meters

Let Length = 4x and breadth = 2x

So, Perimeter: 2 (4x + 2x) = 3000
8x + 4x = 3000
12x = 3000
x= 3000/12= 250 meters

So, Length = 4 * 250 = 1000 meters

And, Breadth = 2 * 250 = 500 meters

Area = Length * Breadth
      = 1000 * 500
      = 50000 sq. m.

Perimeter of Square = 4 x side
4 x side = 24
Side = 24/4 = 6 cm
One of the sides of the square is 6 cm.