 Hello and welcome to the session. In this session we discussed the following question which says in the given figure we have PQ equal to 24 centimeters, PR equal to 7 centimeters and O is the center of the circle, find the area of the shaded region. Let's move on to the solution now. We're given this figure where we have PQ is equal to 24 centimeters, PR is equal to 7 centimeters and we have to find the area of the shaded region. Now angle RPQ is equal to 90 degrees since it is the angle in a semicircle and we know that the measure of the angle in a semicircle is 90 degrees. So this means that the triangle RPQ is a right angled triangle. Now let's consider this triangle in this we have RQ square is equal to RP square plus PQ square since it is the right angled triangle. So we have used the Pythagoras theorem now putting the respective values of PQ and PR we get RQ square is equal to 7 square plus 24 square that is RQ square is equal to 49 plus 576. So RQ square is equal to 625. This gives us the value of RQ equal to square root of 625 which is equal to 25 centimeters since the side cannot be negative. So we have not taken minus 25. Now we take left RBD radius of the circle. So we have R is equal to OR is equal to OQ which is equal to 25 upon 2 centimeters. Now we need to find out the area of the shaded region. So we have area of the shaded region is equal to the area of the semicircle minus area of the triangle RPQ area of the semicircle is equal to half the area of the circle that is half into pi R square. This is equal to half into now we take the value for pi as 3.14 into R which is 25 upon 2 the whole square. And so this is equal to 3.14 into 25 into 25 the whole upon 8 and this is equal to 1962.5 upon 8 which further is equal to 245.31 centimeters square is the area of the semicircle. Now next we find out the area of the triangle RPQ which is equal to half into base which is PR into the height that is PQ. Since it is a right angle triangle we substitute the values for PR and PQ. So this is equal to half into 7 into 24. Now 12 times is 24. So this is equal to 7 into 12 which is equal to 84 centimeters square is the area of the triangle RPQ. Now we know that the area of the shaded region is equal to area of the semicircle minus the area of triangle RPQ. So we have area of the shaded region is equal to 245.31 minus 84 centimeters square and this is equal to 161.31 centimeters square approximately. So thus this is the required answer that is the area of the shaded region is equal to 161.31 centimeters square approximately. So this completes the session that we have understood the solution of this question.