 Hello and welcome to the session. In this session we discussed the following question which says find the area of the shaded region in the given figure that is in this figure and take pi equal to 3.14. So we are given this figure and we have to calculate the area of the shaded region. First let's recall the formula to find out the area of the rectangle. This is equal to L into B where L is the length of the rectangle, B is the depth of the rectangle and the area of the circle is equal to pi R square and this R is the radius of the circle. This is the key idea to be used in this question. Now let's see the solution. Let's first name this rectangle as PQRS. We have the circle with center O and we are also given the dimensions of this rectangle PQRS. So first of all let's find out the area of the rectangle PQRS. This is equal to 4 into 3 centimeter square that is 12 centimeter square is the area of this rectangle. Now since we need to find the area of the shaded region, so from the figure you can see that the area of the shaded region is equal to the area of the circle minus the area of the rectangle PQRS. Now to find the area of the circle we should know it's radius but in this figure we are only given the dimensions of the rectangle, we are not given the radius of the circle. To find the radius of the circle first let's join PR. Now consider the triangle PQR. This is obviously right angle triangle because PQRS is rectangle and so angle PQR would be of measure 90 degrees. So now in right triangle PQR we have PR square is equal to PQ square plus QR square by the Pythagoras theorem. Now this gives us PR square is equal to PQ square that is 4 square plus QR square that is 3 square since we know that PQ is equal to 4 centimeters and QR is equal to 3 centimeters. So further we have PR square is equal to 16 plus 9 that is PR square is equal to 25 which gives us PR equal to square root 25 that is equal to 5 centimeters. So we get the length of PR as 5 centimeters. Now since O is the center of the circle so we have PO is equal to OR and this would be equal to PR upon 2 that is equal to 5 upon 2 centimeters thus we get PO equal to OR is equal to 2.5 centimeters. This means the radius of the circle say R is equal to 2.5 centimeters. Now the area of the circle is equal to pi R square that is pi into 2.5 square centimeters square and this is equal to now taking the value of pi as 3.14 into 2.5 square which is 6.25 centimeters square and this is equal to 19.625 centimeters square is the area of the circle. So we have now got the area of the circle and we also have the area of the rectangle PQRS. So we can easily find out the area of the shaded region. So area of the shaded region is equal to area of the circle which is 19.625 minus the area of rectangle which is 12 centimeters square. So area of shaded region is equal to 19.625 minus 12 centimeters square and this is equal to 7.625 centimeters square. So this is our final answer that is the area of the shaded region is 7.625 centimeters square. This completes the session. Hope you have understood the solution of this question.