In a figure, ob is the radius of a big semicircle and xb is the radius of the small semicircle. given that ox = 14 cm, calculate the area and the perimeter of the shaded region in the figure.
(take π = 22/7).

perimeter of the shaded region = 88 +44+28 =160 cm

Step-by-step explanation:

perimeter of shaded region = length AO + arc OB + arc AB

length AO = radius of bigger circle

radius of bigger circle = OX + OB = 2×radius of smaller circle = 2×14 cm = 28 cm

therefore AO = 28 cm

length of arc oB= half of circumference of smaller circle = ×14 = 44 cm

length of arc ab = half of circumference of bigger circle  = ×28 =×28= 88

therefore perimeter of the shaded region = 88 +44+28 =160 cm

area of the shaded region = half of area of bigger circle - half of area of smaller circle

                                           =

                                           =

  solving we gen area of shaded region = 924

m∠a is 90°

m∠b is 40°