Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the adjoining figure. Find the area of the shaded region.

Explanation

Required area = (area of large semicircle with radius 4.5 cm)
`-` (area of two smaller semicircle with radius of each `(3)/(2) cm` and a circle with radius `(4.5)/(2) cm`) `+` (area of smaller semicircle with radius `(3)/(2) cm`)
`= (1)/(2) pi (4.5)^(2) - [2 xx (1)/(2) pi ((3)/(2))^(2) + pi ((4.5)/(2))^(2)] + [(1)/(2)pi ((3)/(2))^(2)]`
`= (1)/(2) pi (4.5)^(2) - pi ((3)/(2))^(2) - pi ((4.5)/(2))^(2) + (1)/(2) pi ((3)/(2))^(2)`
`= (1)/(4) pi [2 xx (4.5)^(2) - 9 - (4.5)^(2) + (9)/(2)] = (1)/(4) pi xx 4.5 [2 xx 4.5 - 2 - 4.5 + 1]`
`= (1)/(4) pi xx 4.5 (3.5) = (1)/(4) xx (22)/(7) xx 4.5 xx 3.5 = 12.375 cm^(2)`