Question

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).

Answer 1

Answer:

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 = $\pi$×14 = 44 cm

length of arc ab = half of circumference of bigger circle  = $\pi$×28 =$\frac{22}{7}$×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

                                           =$\frac{1}{2} \pi 28^{2} -\frac{1}{2} \pi 14^{2}$

                                           =$\frac{\pi }{2} (28^{2} -14^{2} )$

  solving we gen area of shaded region = 924