 Hi and welcome to the session. Let us discuss the following question. Question says, find the area of the shaded region in figure 12.22, where a circular arc of 6 cm has been drawn with a vertex O of an equilateral triangle OAB of site 12 cm as centre. This is the given figure 12.22. First of all, let us understand that area of sector is equal to theta upon 360 multiplied by pi r square, where theta is the angle of the sector in degrees and r is the radius of the circle. And also, area of equilateral triangle is equal to root 3 upon 4 multiplied by side square. Now we will use these formulas as our key idea to solve the given question. Let us now start with the solution. We are given that triangle OAB is the equilateral triangle and each of its side is equal to 12 cm. And we have to find area of the shaded region. Now clearly we can see area of the shaded region is equal to area of triangle OAB plus area of this sector. Now we know AB is equal to 12 cm or we can say side of equilateral triangle OAB is equal to 12 cm. We also know that area of equilateral triangle is equal to root 3 upon 4 multiplied by square of its site. Now area of equilateral triangle OAB is equal to root 3 upon 4 multiplied by square of 12 cm square. Now this is further equal to root 3 upon 4 multiplied by 12 multiplied by 12 cm square. Now we will cancel common factor 4 from numerator and denominator both and we get 36 root 3 cm square is equal to area of triangle OAB. We also know that all angles of equilateral triangle are equal and each angle is of measure 60 degrees. So we know angle AOB is equal to 60 degrees. Now clearly we can see remaining shaded region is a sector of angle 360 degrees minus 60 degrees. Now this is further equal to 300 degrees. So we get this angle is equal to 300 degrees. We also know that radius of the circle is equal to 6 cm. Now we will find area of sector it is equal to theta upon 360 multiplied by pi r square where theta is the angle of the sector and r is the radius of the circle. We know angle of the sector is equal to 300 degrees and radius of the circle is 6 cm. So we can find area of the given sector by substituting 300 for theta and 6 cm for r in the given formula. We get 300 upon 360 multiplied by 22 upon 7 multiplied by square of 6 cm square. We know value of pi is equal to 22 upon 7. Now this expression can be further written as 300 upon 360 multiplied by 22 upon 7 multiplied by 36 cm square. We know square of 6 is 36. Now 0 will get cancelled by 0 and 36 will cancel 36. And we get 660 upon 7 cm square is equal to area of the given sector. Now we know total area of shaded region is equal to area of triangle OAB plus area of sector of angle 300 degrees. Now substituting corresponding values of area of triangle OAB and area of sector of angle 300 degrees in this expression we get 36 root 3 plus 660 upon 7 cm square is equal to area of shaded region. So this is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.