Question

Read the following passage:

Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will have adequate space for parking. After survey, it was decided to build rectangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and breadth of the rectangular playground are 14 units and 7 units, respectively. There are two quadrants of radius 2 units on one side for special seats.

Based on the above information, answer the following questions:

1. What is the total perimeter of the parking area?
2. (a) What is the total area of parking and the two quadrants?
   OR
   (b) What is the ratio of area of playground to the area of parking area? 
3. Find the cost of fencing the playground and parking area at the rate of ₹ 2 per unit.

Answer 1

i. Given, Length of rectangular playground = 14 units

Breadth of rectangular playground = 7 units

Total perimeter of parking area = Perimeter of semi-circle + Breadth of rectangle

= πR + 7  ...`(("Diameter of semi-circle" = 7),("R" = 7/2))`

= `π xx 7/2 + 7`

= `22/7 xx 7/2 + 7`

= 11 + 7

= 18 units

ii. (a) Given, radius of the quadrant = 2 units

Area of two quadrants = `2 xx ((π"r"^2)/4)`

= `2 xx (π(2)^2)/4`

= 2π sq. units

Area of parking area = `(π"R"^2)/2`

= `π/2 xx (7/2)^2`       ...`(∵ "Radius (R) of semicircle" = 7/2)`

= `22/7 xx 7/2 xx 7/2 xx 1/2`

= `77/4`

= 19.25

Total area of parking and two quadrants

= `2 xx 22/7 + 19.25`

= 6.28 + 19.25

= 25.53 sq. units

OR

(b) Required Ratio = `"Area of playground"/"Area of parking area"`

= `(7 xx 14)/(77/4)`

= `(14 xx 4)/11`

= `56/11`

iii. Perimeter of rectangle part = 2 (Length + Breadth)

= 2 (7 + 14)

= 2 × 21

= 42 units

Perimeter of parking area = πR

= `π xx 7/2`

= `7/2 xx 22/7`

= 11 units

∴ Perimeter of entire region = Perimeter of rectangular part + Perimeter of parking area

= 42 + 11 = 53 units

∴ Cost of fencing = ₹ 2 per unit

∴ Total cost = 53 × 2 = ₹ 106