 Hello and welcome to the session. In this session, I will discuss a question which says that in figure, find the area of the shaded region if A B C D is a rectangle with A B is equal to 80 cm and B C is equal to 70 cm and the A E V is equal to 90 degrees and D E is equal to 42 cm and a semicircle is drawn with B C as a diameter and take pi is equal to 22 by 7. Now before starting the solution of this question, we should know some results. Semi-circle is equal to 1 by 2 into pi r square where r is the radius of the circle. Secondly, the rectangle is equal to length into breadth is equal to 1 by 2 into base into height. In a right angle triangle, B C square is equal to A B square plus B C square. That means height. Now these results will work out as a key idea. We will start with the solution. Another question, we have to find the area of the shaded region and given A B C D is the rectangle with A B is equal to 80 cm, B C is equal to 70 cm, angle A E D is equal to 90 degrees and D E is equal to 42 cm. Also, a semicircle is drawn with B C as a diameter. So given B C D is a rectangle, P is equal to 80 cm, B C is equal to 70 cm, A E D is equal to 90 degrees and D E is equal to 42 cm and we have to take is equal to 22 by 7. Now in a right angle triangle, by Pythagoras theorem, by using this theorem is equal to A E square plus D E square equal to B C is equal to 20 cm because D R, so these will be equal. Now we have equal to 70 cm and D B is equal to 42 cm. So let us know this as equation number one. Now from equation number one, we get by putting the value of A D and is equal to A E square 42 square. A E square is equal to 900 minus 1764. Further this implies A E square is equal to 3136 which further implies A E is equal to 56 cm. Now this is the formula for finding out the area of the triangle. Now area of B D is equal to 1 by 2 into base which is D E into height which is A E to 42 cm which is equal to 56 cm. So putting these values here, this will be equal to 1 by 2 into 42 into 56 cm square. Now here 2 into 21 is 42. So I am calculating this will be equal to 1176 cm square. Now this is the formula for finding out the area of the semicircle. Now let us give this semicircle with B C as the diameter as number one. So area of the semicircle 1 is equal to 1 by 2 into B C is the diameter that is B C which is equal to 70 cm to B C by 2. That is equal to 70 by 2 which is equal to 35 cm. This semicircle 1 is equal to 1 by 2 into pi which is 22 by 7 into 35 into 35 cm square. Now here 2 into 11 is 22 and 7 into 5 is 35 and I am calculating this is equal to 1925 cm square. Now this is the formula for the area of the rectangle. So now the area of rectangle B C D is equal to length into breadth which is A B into B C. That will be 80 into 70 cm square which is equal to 5600 cm square. Now in the shaded portion or shaded region is equal to 2 of the rectangle A B C D minus 2 of triangle A E D minus semicircle 1. Now this is the area of the rectangle A B C D and this is the area of semicircle 1 which is the area of the triangle A E D. Equal to 600 cm square minus 1176 cm square minus 1925 cm square which is further equal to 6 cm square minus 1101 cm square which is further equal to 2499 cm square. Therefore shaded region is equal to 2499 cm square. So this is the solution of the given question and that's all for this session.