**Q) **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 :

(i) What is the total perimeter of the parking area?

(ii) (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?

(iii) Find the cost of fencing the playground and parking area at the rate of Rs. 2 per unit.

**Ans: **

**VIDEO SOLUTION**

**STEP BY STEP SOLUTION**

(i) Perimeter of parking area = outer perimeter of semicircle + diagonal of semicircle

=

Given that, breadth or diameter of semicircle = 7 units

hence,

Therefore, Perimeter of parking area =

**= 18 units**

(ii)(a) Area of parking space and two quadrants = Area of Parking Space + Area of 2 quadrants

Since, both these type of areas have different radius, let’s consider that is the radius of parking space and is the radius of quadrant. We know that:

Since (calculated above)

and (given)

Area of parking space and two quadrants =

Total Area =

= =

**= 25.54 sq. units **

(ii) (b) Ratio of Playground area to Parking area =

= =

**= 56:11**

(iii) Perimeter of required fencing = perimeter of playground + perimeter of parking area

= 2 (l + b) +

= 2(14+7) + x

= 42 + 11 = 53 units

Cost of fencing @ Rs. 2 per unit = 53 x 2

**= Rs. 106**

This completes all the required solutions.