Case Study
Mr Ranveer lives in Agra. He purchased a rectangular plot ABCD to build a house. He leaves a rectangular area ADEF for parking and two congruent semicircular areas to make lower beds, as shown in the figure.

Based on the above information, answer the following questions:

1. Area of the plot left for parking is:
   (a) 24 m²
   (b) 48 m²
   (c) 60 m²
   (d) 63 m²

2. Diameter of each semi-circle is:
   (a) 21 m
   (b) 10.5 m
   (c) 7 m
   (d) 3.5 m

3. Total area of the two semi-circular flower beds is :
   (a) 80.6 m²
   (b) 82.625 m²
   (c) 86.625 m²
   (d) 90.625 m²

4. Area of the plot BCEF is :
   (a) 441 m²
   (b) 400 m²
   (c) 380 m²
   (d) 350 m²

5. Total length of the two semi-circular arcs is :
   (a) 33 m
   (b) 35 m
   (c) 16.5 m
   (d) 54 m

1. Area of plot left for parking is : ADEF

Area of rectangle ADEF = length × breadth

= 3 × 21 = 63 m².

Hence, option (d) is the correct option.

2. The vertical line FE = 21 m.

Two semicircles are placed one above the other and are congruent.

Diameter of each = $\dfrac{21}{2}$ = 10.5 m.

Hence, option (b) is the correct option.

3. Two semi-circles = one full circle

Diameter = 10.5

Radius = $\dfrac{10.5}{2}$ = 5.25 m

Area of circle = πr²

= $\dfrac{22}{7}$ × (5.25)²

= $\dfrac{22}{7}$ × 27.5625

= 86.625 m².

Hence, option (c) is the correct option.

4. Since,

BF = FE = EC = BC = 21 m.

Thus, BCEF is a square.

Area of square BCEF = (side)²

= (21)²

= 441 m².

Hence, option (a) is the correct option.

5. Two semicircles = one circle

∴ Total length of two semicircular arcs = Circumference of one circle = 2πr = πd.

= $\dfrac{22}{7}$ × 10.5

= 22 × 1.5

= 33 m.

Hence, option (a) is the correct option.