 Hello and welcome to the session. In this session we discussed the following question which says the side of a square is 12 centimeters. Find the area of the inscribed circle and the area of the circumscribed circle take pi equal to 3.14. Before we move on to the solution, let's recall the formula to find the area of a circle. This is equal to pi r square where r is the radius of a circle. This is the key idea to be used in this question. Now let's see the solution. We are given that the side of a square is 12 centimeters. Consider this figure where we have this A B C D is the square and each of its side is equal to 12 centimeters. That is we have A B is equal to B C is equal to C D is equal to D A is equal to 12 centimeters. First of all we'll find the area of the inscribed circle and this is equal to pi r square r is the radius of this inscribed circle which is given by say O Q. So pi into O Q square. Now we need to find O Q. As you can see this O is the center of the circle. So P Q is the diameter of the inscribed circle and this would be equal to the side of the square. Therefore we have P Q would be equal to 12 centimeters and so O Q is equal to P Q by 2 that is equal to 6 centimeters. So this is the radius of the inscribed circle thus area of the inscribed circle is equal to pi into 6 square centimeter square that is equal to 36 pi centimeter square. This is equal to 36 into 3.14 centimeter square which comes out to be equal to 113.04 centimeter square. This is the area of the inscribed circle. Now next we find out the area of the circumscribed circle is equal to pi into radius square that is the radius of the circum circle. This is given by say O C. So pi into O C square is the area of the circumscribed circle. Now here A C is the diameter of the circumscribed circle and as you can see in the figure A C is the diagonal of the square and as you know the diagonal of the square is given by root 2 into side that is root 2 into 12 centimeters. So we have A C is equal to 12 root 2 centimeters. Now O C is equal to A C upon 2 as O is the center of the circle. So this is equal to 12 root 2 upon 2 now 2 6 times is 12 so this is equal to 6 root 2 centimeters is equal to O C and this is equal to 8.484 centimeters is O C that is the radius of the circumscribed circle. We have the area of the circumscribed circle is equal to pi into radius square that is pi into 8.484 square centimeters square putting the value for pi. So this is equal to 3.14 into 8.484 square centimeters square and this comes out to be equal to 226.011 centimeters square is the area of the circumscribed circle. Thus we have the area of the inscribed circle is equal to 113.04 centimeters square and the area of the circumscribed circle is equal to 226.011 centimeters square. So this completes our session hope you have understood the solution of this question.