Question

Find the area of the shaded portion

Answer 1

a)

there are given a rectangle.

in which given semicircle

the length of the rectangle (l) = 10 .5 cm

and the breadth of the rectangle (b) = 7 cm

for radius semicircle = 10.5/2 = 5.25cm

So, the area of shaded portion = the area of rectangle - the area of hemisphere

= l× b - 1/2π r ^

= 10.5 × 7 - 1/2 × 22/7 × 5.25^

= 73.5 - 11/7×27.56

= 73.5 -43.30

= 30.2 cm ^

b) In second figure given 4 semicircles and 1 square

the side of square = 14 cm

and the diameter of semicirle (d) = 14 cm

and radius (r) = d /2 = 14/2 = 7 cm

Now area of shaded portion = area of four semicircle + area of square

= 4× 1/2 × π r ^ + a^

= 2 × 22/7 × 7^ + 14 ^

= 44× 7× 7/7 + 196

= 44 × 7 + 196

= 308 + 196

= 504 cm ^