 Hello and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, find the area of the shaded region in figure 12.20 if the radii of two concentric circles with center O are 7 cm and 14 cm respectively and angle AOC is equal to 40 degrees. This is the given figure 12.20. First of all let us understand that area of sector is equal to theta upon 360 multiplied by pi r square. Here theta is the angle made by the sector at the center of the circle and r is the radius of the circle. This is the key idea to solve the given question. Let us now start with the solution. Now we know these two circles are concentric circles that is they have common center O. Now we know that radius of the outer circle is equal to 14 cm, radius of inner circle is equal to 7 cm. This is given in the question. We have to find the area of this shaded region. If we subtract area of sector OVD from area of sector OAC we get area of shaded region AC dB. First of all let us find out area of sector OAC. Now area of sector OAC is equal to 40 degrees upon 360 degrees multiplied by pi multiplied by square of 14. We know area of sector is equal to theta upon 360 degrees multiplied by pi r square. Here theta is the angle made by the sector at the center of the circle and r is the radius of the circle. Now we will find area of sector OBD. This is equal to 40 degrees upon 360 degrees multiplied by pi multiplied by square of 7 cm square. Here radius is equal to 7 cm and we know central angle that is theta is equal to 40 degrees. So substituting corresponding values of theta and r in the formula of area of sector we get area of sector OBD. Now area of shaded region is equal to area of sector OAC minus area of sector OBD. Now substituting corresponding values of area of sector OAC and area of sector OBD in this expression we get area of shaded region is equal to 40 degrees upon 360 degrees multiplied by pi multiplied by square of 14 minus 40 degrees upon 360 degrees multiplied by pi multiplied by square of 7. Now clearly we can see that 40 degrees upon 360 degrees multiplied by pi is common in both the terms. So taking 40 upon 360 multiplied by pi common we get this expression. Now simplifying further we get 1 upon 9 multiplied by pi multiplied by 14 minus 7 multiplied by 14 plus 7 we know a square minus b square is equal to a minus b multiplied by a plus b. Now substituting value of pi in this expression we get 1 upon 9 multiplied by 22 upon 7 we know pi is equal to 22 upon 7 multiplied by 7 multiplied by 21. Now simplifying further we get 1 upon 9 multiplied by 22 upon 7 multiplied by 7 multiplied by 21. Now 7 will cancel 7 and we know 3 multiplied by 3 is equal to 9 and 3 multiplied by 7 is equal to 21. Now this is equal to 154 upon 3 centimeter square. So we get area of this shaded region is equal to 154 upon 3 centimeter square. So this is our required answer this completes the session hope you understood the solution take care and have a nice day.