Let us assume the length as 2x and breadth as 3x.

Now, 1/6 hectares = 1/6 * 10000 = 5000/3 m²

Then, 2x * 3x = 5000/3

6x² = 5000/3

x² = 5000/18 or 2500/9

x = 50/3

Thus, length = 100/3 m

Breadth = 150/3 or 50 m

The Diameter of the circle is equals to the smallest side of the rectangle.

Therefore, diameter = 22 cm.

Then, radius = 22/2 = 11 cm

Area = πr² = 22/7*11*11 = 380.28 cm²

Given, length = 29.5

Given breadth = 21.8

Area of rectangular = l * b = 29.5 * 21.8= 643.1m²

Perimeter of rectangle = 2 * (29.5 + 21.8) = 2 * 51.3

= 102.6 m

Perimeter = Area covered in 8 minutes = 10000/60 * 12

= 2000 m

Let us assume the length as 5x and breadth as 4x.

Then, 2(5x + 4x) = 2000

2(9x) = 2000

18x = 2000

x = 111.11

Then, length = 555.55

Breadth = 444.44

Therefore, area = length * breadth

= 555.55 * 444.44 = 246908.64 m²

Let us assume the length as x, breadth as 3x/2, and height as h.

Then the area of the floor = Cost of flooring/Rate meter per square

= 540/10 = 54 m².

Therefore, x * 3x/2 = 54

x² = 54 * 2/3 = 36

x = 6

Thus, length = 6

Breadth = 3 * 6/2 = 9

Now, area of four walls = Cost of painting/Rate = 3440/20 = 172 m²

Given, area of two windows and one door = 8 m²

Therefore, total area of walls = 172 + 8 = 180 m²

Thus, 180 = 2(l+b) * h

2(6+9)* h = 180

30 * h = 180

30h = 180

h = 6 m

As we know that diagonals of a rhombus bisect at a right angle. Therefore, one side and half of each diagonal form a right angle triangle.



Given, one side = 5 cms

Another side = 8/2 = 4 cms

Third side = (5)² – (4)² = = 3

Therefore, half of the other diagonal is 3

Thus, other diagonal = 3*2 = 6 cms

Hence, area = ½ * 8*6 = 24 cms²

 

Given, AB = 80 m

CD = 50 m

BC = 70 m

AD = 48 m

CE is parallel to AD, therefore, CE = 48 m

Now, AE = CD = 50 m

BE = (AB – AE) = (80-50) = 30 m

CE = AD = 48 m

Then, s = 30 + 70 + 48/2 = 74 m

Area of BCE = ⎷74 * 30 * 70 * 48 = 2731.15 m²

So, ½ * 30 * height = 2731.15

Height 182.07 m

Therefore, area of trapezium = ½ * (80+50) * 182.07 = 11834.55 m²

Therefore, the cost of cultivating = 11834.55 * 95/100 = Rs. 11242.82

Let us assume the original length as x and breadth as y.

Then area = xy

If the side is increased by 42%, then new length = 142/100x = 71x/50

New breadth = 71x/50

Then, new area = 71x/50* 71x/50

= 5041/2500 xy

The difference between new and original area = 5041/2500 xy – xy

= 2541xy/2500

Therefore, percent increase = 2541xy/2500 * 1/xy * 100 = 101.64%

Let us assume PQR as an isosceles triangle and PS as altitude.

Let PQ = PR = x

Then, QR = (40-x)

As we know that in an isosceles triangle the altitude bisects the base,

Then, QS = SR = (20 – x)

In triangle PSR, PR² = PS² + SR²

Then, x² = (10)² + (20 – x)²

x² = 100 + 400 – 40x + x²

40x = 500

x = 25/2

Thus, QR = (40 – 2x) = 40 – 25 = 15

Hence, area = ½ * QR * PS

= ½ * 25/2 * 15 = 93.75 cm²

Area = (total cost)/ (rate/hectare)

Hectares = 1880/117.5 = 16

16 hectares = 160000 m²

Side of the square = 160000 = 400m

Perimeter = 4 * 400 = 1600 m

Cost of fencing = 1600 * 80/100 = Rs. 1280.