Question

9) A rectangular hall has semicircular walls on its
two sides, as shown. If the dimensions of the
rectangular portion are 12 metres and 7 metres
calculate the area covered by the hall.​

Answer 1

Answer:

122.5 m²

Step-by-step explanation:

Area of figure = Area of rectangle + area of 2 semi-circle of diameter(=breadth).

Radii of semi-circle = breadth/2 = 7/2

Area of 2 semi-circle = 2[ 1/2 π(7/2)² ]

                            = 38.5 m²

Area of rectangle = length x breadth

                          = 12 x 7 = 84 m²

Total area covered by the hall = 38.5 + 72 m² = 122.5 m²

Answer 2

area covered by the hall is 122.5 m²

length of rectangle , l = 12m

breadth of rectangle, b = 7m

radius of semicircle, r = 7/2 m = 3.5 m

area covered by the hall = 2 × area of semicircular + area of rectangle

= 2 × πr²/2 + l × b

= πr² + l × b

= 22/7 × (3.5)² + 12 × 7

= 22 × 0.5 × 3.5 + 84

= 11 × 3.5 + 84

= 38.5 + 84

= 122.5 m²